A Delivery Robot Charging Scheduling Method Based on Aggregation Game Theory

Abstract

This invention discloses a charging scheduling method for delivery robots based on aggregation game theory, belonging to the field of delivery robot charging scheduling. This invention uses an L-BPNN neural network with linear mapping relationships to construct a distributed charging cost optimization model for intelligent delivery robots; it employs aggregation game theory to solve the distributed charging cost model optimization problem, effectively utilizing the non-cooperative nature and mutual influence among feature data variables to improve the accuracy and efficiency of charging scheduling; in the charging scheduling aggregation game process, a global guidance variable is introduced, and each delivery robot simultaneously updates its own charging strategy based on the global guidance variable, significantly shortening the time required for the charging scheduling aggregation game process to reach Nash equilibrium, while avoiding deviation problems caused by excessive pursuit of low cost; the L-BPNN neural network parameters of the intelligent delivery robot distributed charging optimization model are iteratively optimized through a genetic algorithm, improving the prediction accuracy and efficiency of the intelligent delivery robot distributed charging optimization model.

Description

Technical Field

[0001] This invention belongs to the field of delivery robot charging scheduling, and relates to a multi-objective optimization method for delivery robot charging scheduling with spatiotemporal coupling constraints. Background Technology

[0002] In China, hospitals are operating at high capacity, and the distribution of medical supplies has always been an extremely tedious and demanding task. With the development of technology, new logistics equipment such as intelligent delivery robots for hospitals have effectively solved the existing difficulties in hospital supply distribution. At the same time, the maturity of 5G networks has also promoted the rapid development of intelligent delivery robots.

[0003] After determining the deployment plan for intelligent delivery robots and resolving the optimization issues regarding the number and location of charging stations, the charging decisions for these robots become a crucial issue requiring further research to ensure their power supply and the effective operation of the delivery system. Charging scheduling is related to the rational allocation of power resources. When the workload is heavy and tasks are urgent, high-power fast charging is necessary, even at the cost of battery durability, to ensure smooth delivery. Conversely, when there is a long idle period and low task frequency, low-power slow charging can replenish the remaining charge (SOC). Therefore, an optimal charging scheduling scheme based on charging time and charging power can not only ensure the smooth operation of delivery tasks but also achieve the rational utilization of resources.

[0004] Charging scheduling is a problem of finding the optimal charging scheme under the constraints of task conditions and robot SOC (State of Charge). A reasonable SOC is a prerequisite for the smooth execution of tasks by the delivery robot, and the optimal charging cost needs to be achieved while ensuring smooth task execution. Fast charging provides sufficient power in a short time, allowing for more tasks to be performed, but it reduces battery life; slow charging is beneficial for long-term battery use, but the frequency of task execution is significantly reduced. For the charging scheduling problem, the delivery robot needs to coordinate the status of charging terminals based on charging cost and task volume. Furthermore, charging scheduling needs to consider not only charging cost but also the current status indicators of various information within the hospital, urgent public medical events, and predicted power demand in various departments' operations, to implement a unified dynamic charging scheduling deployment for the delivery system. Therefore, for the charging scheduling problem of delivery robots with time constraints, spatial constraints, and spatiotemporal coupling constraints, it is urgent to establish a charging scheduling scheme for charging time and charging power to achieve rational resource utilization. Summary of the Invention

[0005] To address the charging scheduling problem of intelligent delivery robots, this invention primarily aims to provide a charging scheduling method for delivery robots based on game theory. It employs an L-BPNN neural network with linear mapping relationships to construct a distributed charging cost optimization model for intelligent delivery robots, making this model more closely reflect the actual operating conditions of intelligent delivery robot charging scheduling. Aggregate game theory is used to solve the optimization problem of the distributed charging cost model, effectively utilizing the non-cooperative nature and mutual influence among feature data variables to improve the accuracy and efficiency of intelligent delivery robot charging scheduling. During the aggregate game process of intelligent delivery robot charging scheduling, a global guidance variable is introduced, and each delivery robot simultaneously updates its own charging strategy based on the global guidance variable, significantly shortening the computation time required to reach Nash equilibrium in the aggregate game process, while avoiding deviations caused by each robot excessively pursuing low costs. The parameters of the L-BPNN neural network in the distributed charging optimization model of intelligent delivery robots are iteratively optimized using a genetic algorithm, improving the prediction accuracy and efficiency of the distributed charging optimization model. This invention achieves high-precision and high-efficiency planning for delivery robot charging scheduling based on game theory, ensuring optimal deployment of intelligent delivery robot resources under different operating conditions.

[0006] The objective of this invention is achieved through the following technical solution.

[0007] This invention discloses a charging scheduling method for delivery robots based on game theory. The method involves analyzing and selecting sample data from the charging scheduling data of intelligent delivery robots, and preprocessing and filtering the sample data to obtain valid sample data excluding missing or outliers. A Pearson chi-square test is used to perform correlation analysis on the valid sample data to identify characteristic data variables that influence the charging results of the intelligent delivery robots. These characteristic data variables include the number of delivery robots, their location distribution, delivery timeliness, remaining battery power, delivery workload, and the number and location distribution of charging stations. A dataset is constructed based on these influential characteristic data variables to build a distributed charging cost optimization model for the intelligent delivery robots. Analysis shows that the characteristic data variables and the charging scheduling results of the intelligent delivery robots have both non-linear and linear relationships. An L-BPNN neural network with linear mapping is selected to construct the distributed charging cost optimization model for the intelligent delivery robots, making the model more closely reflect the actual charging scheduling conditions of the intelligent delivery robots. The distributed charging cost model for intelligent delivery robots is further improved by combining practical constraints. Aggregate game theory is used to solve the optimization problem of the distributed charging cost model for intelligent delivery robots, effectively utilizing the non-cooperative nature and mutual influence among characteristic data variables to improve the accuracy and efficiency of charging scheduling for intelligent delivery robots. In the aggregate game process of intelligent delivery robot charging scheduling, a global guiding variable is introduced, and each delivery robot updates its own charging strategy simultaneously based on the global guiding variable. This significantly shortens the computation time required to reach Nash equilibrium in the aggregate game process of intelligent delivery robot charging scheduling, while avoiding deviation problems caused by each robot excessively pursuing low costs. These deviation problems include robots frequently charging to reduce charging costs. Based on the optimization results of the aggregate game of intelligent delivery robot charging scheduling, the L-BPNN neural network parameters of the distributed charging optimization model for intelligent delivery robots are iteratively optimized using a genetic algorithm, improving the prediction accuracy and efficiency of the distributed charging optimization model for intelligent delivery robots. In other words, based on game theory, high-precision and high-efficiency planning of delivery robot charging scheduling is achieved, ensuring that intelligent delivery robot resources reach optimal deployment under different operating conditions.

[0008] This invention discloses a charging scheduling method for delivery robots based on game theory, comprising the following steps:

[0009] Step 1: Analyze, preprocess, and filter the existing charging scheduling data of intelligent delivery robots to construct a dataset for a distributed charging cost optimization model of intelligent delivery robots, and then construct the distributed charging cost optimization model of intelligent delivery robots through an L-BPNN neural network.

[0010] The specific implementation method of the distributed charging cost optimization model for the intelligent delivery robot in step one is as follows:

[0011] Step 1.1: Analyze existing charging scheduling data for intelligent delivery robots and select sample data. Perform data preprocessing and filtering to obtain valid sample data that does not contain missing or anomalies. This effectively filters out valid sample data from a large amount of data, minimizing the impact of invalid sample data on the establishment of the distributed charging cost optimization model for intelligent delivery robots.

[0012] This paper analyzes and evaluates typical cases of charging scheduling for delivery robots in various scenarios, utilizing available charging scheduling data for intelligent delivery robots. This data includes the number of delivery robots, their location distribution, delivery timeliness, remaining battery power, delivery workload, and the number and location distribution of charging stations. For data under different operating conditions, historical sample data is cleaned through data preprocessing to address data issues in historical order samples caused by other reasons. The preprocessing methods include interpolation, fitting, and data removal. These other reasons include data transfer errors and human error in recording. Data issues include missing data and data anomalies. This effectively filters out valid sample data from a large dataset, minimizing the impact of invalid sample data on the establishment of a distributed charging cost optimization model for intelligent delivery robots.

[0013] Step 1.2: For the valid sample data obtained in Step 1.1, a correlation analysis is performed on the valid sample data using the Pearson chi-square test to screen out the feature data variables that can affect the charging results of the intelligent delivery robots, and a dataset is constructed. This effectively removes feature data variables that do not affect the charging effect of the intelligent delivery robots, accelerates the learning speed of the neural network, and indirectly improves the efficiency of establishing a distributed charging cost optimization model for intelligent delivery robots. The feature data variables include the number of delivery robots, the location distribution of delivery robots, the delivery timeliness of delivery robots, the remaining battery power of delivery robots, the delivery workload of delivery robots, and the number and location distribution of charging piles.

[0014] Pearson's chi-square test was used to screen for characteristic data variables that could influence the charging results. The null hypothesis was that the number of delivery robots was statistically independent of the charging results. Then, a contingency table was compiled. The contingency table is as follows: OK Column, theoretical number of times as follows:

[0015] (1)

[0016] in Given the sample size, then calculate the statistics. :

[0017] (2)

[0018] Based on the set confidence level, the degrees of freedom were determined. The chi-square distribution critical value is compared with the statistical value. If the statistical value is large, the null hypothesis cannot be rejected, meaning that the characteristic data variable is statistically independent of the charging result. Similarly, the statistical independence of the charging scheduling data of all intelligent delivery robots from the charging result can be obtained, thus identifying the characteristic data variables that can influence the charging result. The charging scheduling data includes the number of delivery robots, their location distribution, delivery timeliness, remaining battery power, delivery workload, and the number and location distribution of charging stations. The characteristic data variables include the number of delivery robots, their location distribution, their delivery timeliness, their remaining battery power, their delivery workload, and the number and location distribution of charging stations.

[0019] Then, based on the feature data variables that affect the charging results, a dataset is constructed for building a distributed charging cost optimization model for intelligent delivery robots. This effectively reduces feature data variables that do not affect the charging effect of intelligent delivery robots, accelerates the learning speed of neural networks, and improves the efficiency of building a distributed charging cost optimization model for intelligent delivery robots.

[0020] Step 1.3: For the dataset obtained in Step 1.2, construct a distributed charging cost optimization model for the intelligent delivery robot using an L-BPNN neural network. This makes the distributed charging cost optimization model for the intelligent delivery robot more closely reflect the actual charging scheduling conditions of the intelligent delivery robot.

[0021] A distributed charging optimization model for intelligent delivery robots is established using deep learning methods. BPNN possesses excellent nonlinear mapping capabilities, strong self-learning ability, good generalization ability, and superior fault tolerance. Its most prominent advantage is its nonlinear mapping capability, meaning that complex nonlinear mapping relationships between input and output can be obtained simply through modeling without prior knowledge of the specific mathematical relationships. However, the relationship between charging efficiency and feature data variables is not merely nonlinear. Analysis reveals that the relationship between these feature data variables and the charging scheduling results of the intelligent delivery robot exhibits both nonlinear and linear relationships—a combination of both. In this case, BPNN may not be able to fully and accurately represent the relationship. Therefore, it is necessary to improve the BPNN from the network topology perspective, obtaining a BPNN with linear mapping relationships, namely L-BPNN. The L-BPNN neural network with linear mapping relationships is selected to construct the distributed charging cost optimization model for the intelligent delivery robot, making the model more closely reflect the actual charging scheduling conditions of the intelligent delivery robot.

[0022] The L-BPNN neural network structure adds a direct connection between the input and output layers to the BPNN, reflecting the linear and nonlinear relationship between the input and output. This indicates the input information. Indicates a hidden layer. Indicates the output value. This represents the weights between the input layer and the hidden layer. This represents the weights between the hidden layer and the output layer. This represents the weights between the input and output layers. Therefore, the expression for calculating the output of the L-BPNN hidden layer remains:

[0023] (3)

[0024] In the formula This represents the activation function of the hidden layer; the sigmoid function is commonly used. Indicates the number of neurons in the hidden layer. This indicates the hidden layer bias.

[0025] The expression for the corresponding output layer can be represented as:

[0026] (4)

[0027] In the formula Indicates the number of neurons in the output layer. This indicates the output layer bias.

[0028] The prediction framework for the distributed charging cost optimization model of intelligent delivery robots based on L-BPNN also includes four parts: the establishment of network topology and the initialization of relevant parameters, the learning and training of L-BPNN, obtaining the optimal network parameters, and the prediction of the distributed charging cost optimization model of intelligent delivery robots.

[0029] After establishing a delivery robot deployment optimization model using L-BPNN, a constraint model and optimization metrics based on charging time and power costs are established, based on real-time information of feature variables. The real-time information of feature variables includes current task volume, delivery timeliness, and the number and location distribution of charging stations. The optimization sub-problems are defined as follows:

[0030]

[0031] st (5)

[0032] and

[0033]

[0034] st (6)

[0035] in, The charging time cost under scheduling, The cost of charging power under scheduling, For the current workload, For the remaining delivery time, To determine the distance to the charging station under the dispatching system. This represents the robot's maximum battery capacity.

[0036] Step Two: Further refine the distributed charging cost model for the intelligent delivery robot constructed in Step One by combining it with constraints based on actual conditions. This is beneficial for the application of this invention in real-world production and daily life. Aggregate game theory is selected to solve the optimization problem of the distributed charging cost model for the intelligent delivery robot. Aggregate game theory effectively utilizes the non-cooperative nature and mutual influence among characteristic data variables to improve the accuracy and efficiency of charging scheduling for the intelligent delivery robot. In the aggregate game process of intelligent delivery robot charging scheduling, a global guiding variable is introduced, and each delivery robot updates its own charging strategy simultaneously based on the global guiding variable. This significantly shortens the computation time required for the aggregate game process of intelligent delivery robot charging scheduling to reach Nash equilibrium, while avoiding deviation problems caused by each robot excessively pursuing low costs. These deviation problems include robots frequently charging to reduce charging costs.

[0037] Step 2.1: Based on the distributed charging cost optimization model for the intelligent delivery robot obtained in Step 1, further improve the model by combining it with the constraints of the actual situation.

[0038] First, the problem is further improved and optimized by combining the constraints based on the actual situation, so as to obtain a more suitable charging scheduling scheme. The constraints based on the actual situation include task frequency and battery remaining SOC index.

[0039] Considering practical realities, delivery tasks generally operate within a relatively stable range. To better reflect actual working conditions, task frequency needs to be constrained. When a battery is completely depleted during use, it causes severe battery discharge, damaging the internal electrode plates. Therefore, each instance of over-discharge damages the battery's internal electrode plates. Each recharge after severe discharge causes the charger's input current to accelerate, leading to excessive heat and damage, even deformation and detachment of the electrode plates from the acid. This also affects the battery's normal charge storage capacity, directly shortening its lifespan. Furthermore, severe deformation and detachment of the internal electrode plates after complete discharge can cause premature false saturation during charging, resulting in short-lived charge. Therefore, to extend battery life, the remaining charge level during charging needs to be constrained.

[0040] st (7)

[0041] Step 2.2: An aggregate game theory approach is used to solve the distributed charging cost model optimization problem for intelligent delivery robots. This effectively utilizes the non-cooperative nature and mutual influence among characteristic data variables to improve the accuracy and efficiency of charging scheduling for intelligent delivery robots. In the aggregate game process of intelligent delivery robot charging scheduling, a global guidance variable is introduced, and each delivery robot updates its own charging strategy simultaneously based on this global guidance variable. This significantly shortens the computation time required to reach Nash equilibrium in the aggregate game process of intelligent delivery robot charging scheduling, while avoiding deviation problems caused by each robot excessively pursuing low costs. The optimized result of the aggregate game theory approach for intelligent delivery robot charging scheduling is then output. The deviation problem includes robots frequently charging to reduce charging costs.

[0042] Aggregation game theory requires establishing a game model, designing global guiding variables, and then solving for the Nash equilibrium strategy. Based on the battery characteristics of delivery robots, charging strategies, and the non-cooperative and mutually influential power resource requirements of different robots, a cost function for the charging game is established.

[0043] Multi-player aggregate games are described using three basic elements: participants, strategy set, and cost function. Represents the set of tags for participants, using Indicates the first The set of strategies of each participant, and using Represent the decision variables for this participant. (Used as...) Indicates the first The cost function of each participant, where

[0044] (8)

[0045] (9)

[0046] They represent the exceptions All decision variables and all strategy combinations except The set For each , No. The goal of each participant is to address the current situation. Choose decision variables This makes the cost function To reach the minimum. Furthermore, for convergent games, there is also a convergent mapping. Defined as

[0047] (10)

[0048] in Map local decision variables to aggregate terms. Furthermore, the cost function satisfies...

[0049] (11)

[0050] (12)

[0051] in , ;

[0052] Furthermore, the average charging strategy of the delivery robot ensemble is used as a global guiding variable, and each delivery robot simultaneously updates its own charging strategy based on this global guiding variable. This mechanism is very simple; the computation time required to reach Nash equilibrium is independent of the number of participating robots.

[0053] Step 3: Based on the intelligent delivery robot charging scheduling aggregation game optimization results described in Step 2, the parameters of the L-BPNN neural network of the intelligent delivery robot distributed charging optimization model are iteratively optimized through a genetic algorithm to improve the prediction accuracy and efficiency of the intelligent delivery robot distributed charging optimization model. That is, based on game theory, high-precision and efficient planning of delivery robot charging scheduling is realized, so that the intelligent delivery robot resources can achieve optimal deployment under different working conditions.

[0054] The optimization part of the genetic algorithm is the weights between the input layer and the hidden layer. and hidden layer bias Weights between hidden layers and output layers and output layer bias and the weights between the input and output layers. .

[0055] The neural network is used as the main function of the genetic algorithm, and the error function of the L-BPNN neural network is set as the fitness function. The population size is equivalent to the number of effective samples. The fitness of a single individual is The probability of it being selected is:

[0056] (13)

[0057] The individual entity refers to the weights between the input layer and the hidden layer. and hidden layer bias Weights between hidden layers and output layers and output layer bias The binary representation of the model is used. After initial setup, crossover and mutation operations are performed to obtain offspring. Finally, the fitness of each individual is calculated to retain the optimal individual from each iteration, thus optimizing the parameters of the L-BPNN neural network in the distributed charging optimization model for intelligent delivery robots. This improves the prediction accuracy and efficiency of the model, achieving high-precision and efficient planning for delivery robot charging scheduling based on game theory, ensuring optimal deployment of intelligent delivery robot resources under different working conditions. The optimal individual refers to the weights between the optimal input layer and hidden layer of the L-BPNN neural network in the intelligent delivery robot deployment optimization model, charging pile quantity optimization model, and single-layer charging pile location model. and hidden layer bias Weights between hidden layers and output layers and output layer bias .

[0058] It also includes step four: Based on the distributed charging task conditions of the intelligent delivery robot, and following steps one to three, the distributed charging plan for the intelligent delivery robot is carried out. Under the task conditions of numerous tasks, scarce key resources, and spatially separated and scattered task execution locations, the introduction of global guidance variables avoids deviation problems caused by each robot excessively pursuing low costs, improves the charging scheduling accuracy and efficiency of the delivery robot, extends charging life, and improves resource utilization.

[0059] Beneficial effects:

[0060] 1. This invention discloses a charging scheduling method for delivery robots based on game theory. This method is a multi-objective optimization charging scheduling method for delivery robots with spatiotemporal coupling constraints. It analyzes existing charging scheduling data for intelligent delivery robots, selects sample data, and performs data preprocessing to filter out valid sample data that does not contain missing data or anomalies and thus affects the charging results. This effectively filters out valid sample data that affects the charging results from a large amount of data, minimizing the impact of invalid sample data on establishing a distributed charging cost optimization model for intelligent delivery robots.

[0061] 2. The present invention discloses a charging scheduling method for delivery robots based on game theory. It uses an L-BPNN neural network with linear mapping relationship to construct a distributed charging cost optimization model for intelligent delivery robots, so that the distributed charging cost optimization model for intelligent delivery robots is more in line with the actual working conditions of charging scheduling of intelligent delivery robots.

[0062] 3. This invention discloses a charging scheduling method for delivery robots based on game theory. It employs aggregate game theory to establish a game model, designs global guiding variables, and then solves for Nash equilibrium. This effectively utilizes the non-cooperative nature and mutual influence among characteristic data variables to improve the accuracy and efficiency of charging scheduling for intelligent delivery robots.

[0063] 4. The present invention discloses a charging scheduling method for delivery robots based on game theory. The average charging strategy of the group of delivery robots is used as a global guiding variable. Each delivery robot updates its own charging strategy simultaneously according to the global guiding variable. Under this mechanism, the computation time required to reach Nash equilibrium is independent of the number of participants in the game, thereby improving optimization efficiency.

[0064] 5. The present invention discloses a charging scheduling method for delivery robots based on game theory. By iteratively optimizing the parameters of the L-BPNN neural network of the distributed charging optimization model of intelligent delivery robots through genetic algorithm, the prediction accuracy and efficiency of the distributed charging optimization model of intelligent delivery robots are improved. That is, based on game theory, high-precision and efficient planning of charging scheduling for delivery robots is achieved, so that the resources of intelligent delivery robots can be optimally deployed under different working conditions.

[0065] 6. The optimized dynamic deployment of the number and location of charging piles for delivery robots is a prerequisite for the reliable operation of the system. The charging scheduling method for delivery robots based on game theory disclosed in this invention can reasonably arrange charging piles on the basis of achieving the above-mentioned beneficial effects 1 to 5. This can prevent insufficient power and avoid the problem of redundant and idle charging piles, thereby achieving reasonable allocation and efficient utilization of resources. Attached Figure Description

[0066] Figure 1This is a flowchart of a charging scheduling method for delivery robots based on game theory, according to the present invention.

[0067] Figure 2 This is a flowchart of the L-BPNN neural network.

[0068] Figure 3 This is the flowchart of the genetic algorithm.

[0069] Figure 4 shows the effect of charging scheduling. Among them, 4(a) is the initial position distribution of the robot and charging piles, 4(b) is the charging time of each charging pile, 4(c) is the expected number of charging times and the actual number of charging times of each charging pile, 4(d) is the change in the difference between the expected number of charging times and the actual number of charging times of a single charging pile, and 4(e) is the change in the difference in the charging time of a single charging pile. Detailed Implementation

[0070] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0071] Example 1:

[0072] This embodiment discloses a multi-objective optimization charging scheduling method for delivery robots with spatiotemporal coupling constraints, which is applied to the modern intelligent medical delivery system of a general hospital with many departments, scarce key resources, and separate and scattered pharmacies and wards.

[0073] like Figure 1 As shown in the figure, this embodiment discloses a multi-objective optimization charging scheduling method for delivery robots with spatiotemporal coupling constraints. The specific implementation steps are as follows:

[0074] Step 1: Construct a distributed charging cost optimization model for intelligent delivery robots;

[0075] Step 1.1: Analyze and evaluate typical cases of charging scheduling for delivery robots in various scenarios. Using the available charging scheduling data of intelligent delivery robots, clean the selected historical sample data through interpolation, fitting, and elimination to finally obtain effective sample data.

[0076] Step 1.2: Use Pearson's chi-square test to screen for characteristic data variables that can influence the charging results and construct a dataset. The "null hypothesis" is that the number of delivery robots is statistically independent of the charging results. Then, compile contingency tables. The contingency table is as follows: OK Column, theoretical number of times The calculation is as follows:

[0077] (1)

[0078] in The sample size is the sum of all fields in the contingency table. For data in a contingency table, calculate the statistical values. :

[0079] (2)

[0080] Based on the set confidence level, the degrees of freedom were determined. The chi-square distribution critical value is compared with the statistical value. The statistical value is relatively small, so the null hypothesis is rejected, meaning that this feature data variable is correlated with the charging result. Similarly, the statistical independence of the charging scheduling data of all intelligent delivery robots from the charging result can be obtained, thus identifying the feature data variables that can affect the charging result.

[0081] Then, based on the feature data variables that affect the charging results, a dataset is constructed to build a distributed charging cost optimization model for intelligent delivery robots. Considering that the number of effective sample data also affects the training effect and training speed of the neural network, when the effective sample data is too large, the sample data can be sampled and the dataset can be reconstructed.

[0082] Step 1.3: Construct a distributed charging cost optimization model for intelligent delivery robots using an L-BPNN neural network.

[0083] Figure 2 The network structure in the diagram is based on BPNN, with the addition of direct connections between the input and output layers. This reveals the linear and non-linear relationships between the input and output. (See diagram.) This indicates the input information. Indicates a hidden layer. Indicates the output value. This represents the weights between the input layer and the hidden layer. This represents the weights between the hidden layer and the output layer. This represents the weights between the input and output layers. Therefore, the expression for calculating the output of the L-BPNN hidden layer remains:

[0084] (3)

[0085] In the formula This represents the activation function of the hidden layer; here, the sigmoid function is used. Indicates the number of neurons in the hidden layer. This indicates the hidden layer bias.

[0086] The expression for the corresponding output layer can be represented as:

[0087] (4)

[0088] In the formula Indicates the number of neurons in the output layer. This indicates the output layer bias.

[0089] The predictive framework for the distributed charging cost optimization model of intelligent delivery robots based on L-BPNN also includes four parts: establishing the network topology and initializing relevant parameters, learning and training the L-BPNN, obtaining the optimal network parameters, and predicting the distributed charging cost optimization model of intelligent delivery robots. Specific details are as follows... Figure 3 As shown.

[0090] After establishing a delivery robot deployment optimization model using L-BPNN, a constraint model and optimization indices based on real-time information of characteristic variables such as current task volume, delivery timeliness, and the number and location distribution of charging stations are established. The optimization sub-problems are defined as follows:

[0091]

[0092] st (5)

[0093] and

[0094]

[0095] st (6)

[0096] in, The charging time cost under scheduling, The cost of charging power under scheduling, For the current workload, For the remaining delivery time, To determine the distance to the charging station under the dispatching system. This is the robot's maximum battery capacity. The power consumption of the delivery robot, The maximum workload that the robot can perform while charging. This is the robot's current remaining battery power. This is the time required for the robot to travel to the charging station. The significance of this constraint is to ensure that the robot can prioritize completing its tasks when it has sufficient battery power, and to employ optimal charging scheduling when delivery time permits.

[0097] Step 2: Refine and solve the distributed charging cost model of the constructed intelligent delivery robot.

[0098] Step 2.1: First, further refine and optimize the problem based on the constraints based on the actual situation.

[0099] Considering practical realities, delivery tasks generally operate within a relatively stable range. To better reflect actual working conditions, task frequency needs to be constrained. When a battery is completely depleted during use, it causes severe battery discharge, damaging the internal electrode plates. Therefore, each instance of over-discharge damages the battery's internal electrode plates. Each recharge after severe discharge causes the charger's input current to accelerate, leading to excessive heat and damage, even deformation and detachment of the electrode plates from the acid. This also affects the battery's normal charge storage capacity, directly shortening its lifespan. Furthermore, severe deformation and detachment of the internal electrode plates after complete discharge can cause premature false saturation during charging, resulting in short-lived charge. Therefore, to extend battery life, the remaining charge level during charging needs to be constrained.

[0100] st (7)

[0101] in For the delivery task frequency of the delivery robot, and These are the minimum delivery frequency and the maximum delivery frequency, respectively. As mentioned earlier, this refers to the remaining battery power of the delivery robot. The State of Charge (SOC) is the remaining battery charge, which is generally no more than 0.2 considering the battery's lifespan. In this example, there are 3 charging stations and 64 delivery locations, all of which have been initially determined, as shown in Figure 4(a).

[0102] Step 2.2: Use aggregate game theory to solve the optimization problem of the distributed charging cost model of intelligent delivery robots.

[0103] Aggregation game theory requires establishing a game model, designing global guiding variables, and then solving for the Nash equilibrium strategy. Based on the battery characteristics of delivery robots, charging strategies, and the non-cooperative and mutually influential power resource requirements of different robots, a cost function for the charging game is established.

[0104] Multi-player aggregate games can be described using three basic elements: participants, strategy set, and cost function. The participants, i.e., the set of tags for the delivery robots, are represented in this example. ,use Indicates the first A set of strategies for delivery robots, and using Let represent the decision variables for this delivery robot. and They represent the first The timing cost function and power cost function of a delivery robot, where

[0105] (8)

[0106] (9)

[0107] They represent the exceptions All decision variables and all strategy combinations except The set For each , No. The goal of this delivery robot is to address the current... Choose decision variables This makes the cost function and To reach the minimum. Furthermore, for convergent games, there is also a convergent mapping. Defined as

[0108] (10)

[0109] in Mapping local decision variables to aggregate terms. This is the average charging strategy of the delivery robot group, which is used as a global guiding variable. Each delivery robot updates its own charging strategy simultaneously based on this global guiding variable. Furthermore, the cost function satisfies the constraints...

[0110] (11)

[0111] (12)

[0112] in The delivery robot updates its charging strategy based on its own situation. The delivery robot updates its charging strategy based on global guidance variables.

[0113] The scheduling effect is shown in Figure 4. Figure 4(b) shows the charging time of each charging pile, where the red line represents the expected longest charging time of 2.5 hours and the green line represents the expected minimum charging time of 1.5 hours. Figure 4(c) shows the expected number of charging times and the actual number of charging times for each charging pile. The expected number of charging times refers to the number of times the delivery robot is expected to charge to meet the delivery task requirements. Figure 4(d) shows the change in the difference between the expected number of charging times and the actual number of charging times for a single charging pile. The horizontal axis represents the number of iterations. It can be clearly seen that the difference between the expected number of charging times and the actual number of charging times for a single charging pile decreases rapidly with iteration. Figure 4(e) shows the change in the difference in the charging time for a single charging pile. The horizontal axis is still the number of iterations. It can be clearly seen that the difference in the charging time for a single charging pile converges to 0 with the change in iteration, that is, the charging time of a single charging pile tends to stabilize.

[0114] Step 3: Based on the optimization results of the intelligent delivery robot charging scheduling aggregation game, the parameters of the L-BPNN neural network of the intelligent delivery robot distributed charging optimization model are iteratively optimized using a genetic algorithm.

[0115] The optimization part of the genetic algorithm is the weights between the input layer and the hidden layer. and hidden layer bias Weights between hidden layers and output layers and output layer bias and the weights between the input and output layers. The specific algorithm flow is as follows: Figure 3 As shown.

[0116] The neural network is used as the main function of the genetic algorithm, and the error function of the L-BPNN neural network is set as the fitness function. The population size is equivalent to the number of effective samples. The fitness of a single individual is The probability of it being selected is:

[0117] (13)

[0118] After that, crossover and mutation operations are performed to obtain offspring. Here, the crossover probability is selected as 0.7 and the mutation probability is selected as 0.01. Finally, the best individual in each iteration is retained by calculating the fitness of the individual.

[0119] It's important to note here that the first point concerns the number of variables: the input layer has... There are 10 neurons, and the hidden layer has 100 neurons. There are neurons, and the output layer has _____ neurons. One, then There is indivual, have indivual; have indivual, have indivual; have There are a total of [number] [items]. There are parameters, among which

[0120] (14)

[0121] Secondly, regarding population initialization: setting This population Each population contains There are several variables, all of which need to be represented in binary. Therefore, during initialization, it is necessary to generate... A matrix of dimensionality.

[0122] To illustrate the effectiveness of this invention, Figure 4 shows the effect of charging scheduling for delivery robots under simulation conditions. As can be seen from the figure, the charging scheduling of this invention can improve the prediction accuracy and efficiency of the distributed charging optimization model for intelligent delivery robots. Specifically, it achieves high-precision and efficient planning of charging scheduling for delivery robots based on game theory, enabling optimal deployment of intelligent delivery robot resources under different operating conditions.

[0123] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A charging scheduling method for delivery robots based on aggregation game theory, characterized in that: Includes the following steps, Step 1: Analyze, preprocess, and filter the existing charging scheduling data of intelligent delivery robots to construct a dataset for a distributed charging cost optimization model of intelligent delivery robots, and construct the distributed charging cost optimization model of intelligent delivery robots through an L-BPNN neural network. The specific implementation method of the distributed charging cost optimization model for intelligent delivery robots is as follows: Step 1.1: Analyze the existing charging scheduling data of intelligent delivery robots and select sample data. Perform data preprocessing and screening on the sample data to obtain valid sample data that does not contain missing data or anomalies. This effectively filters out valid sample data from a large amount of data and minimizes the impact of invalid sample data on the establishment of the distributed charging cost optimization model for intelligent delivery robots. This paper analyzes and evaluates typical cases of charging scheduling for delivery robots in various scenarios, utilizing available charging scheduling data for intelligent delivery robots. This data includes the number of delivery robots, their location distribution, delivery timeliness, remaining battery power, delivery workload, and the number and location distribution of charging stations. For data under different operating conditions, historical sample data is cleaned using data preprocessing methods to address data issues in historical order samples caused by other reasons. These preprocessing methods include interpolation, fitting, and data removal. Other reasons include data transfer errors and human error in recording. Data issues include missing data and data anomalies. This effectively filters out valid sample data from a large dataset, minimizing the impact of invalid sample data on the establishment of a distributed charging cost optimization model for intelligent delivery robots. Step 1.2: For the valid sample data obtained in Step 1.1, a correlation analysis is performed on the valid sample data using the Pearson chi-square test to screen out the feature data variables that can affect the charging results of the intelligent delivery robot, and a dataset is constructed. This effectively reduces the feature data variables that do not affect the charging effect of the intelligent delivery robot, accelerates the learning speed of the neural network, and indirectly improves the efficiency of establishing a distributed charging cost optimization model for the intelligent delivery robot. The feature data variables include the number of delivery robots, the location distribution of delivery robots, the delivery timeliness of delivery robots, the remaining battery power of delivery robots, the delivery workload of delivery robots, and the number and location distribution of charging piles. Pearson's chi-square test was used to screen for characteristic data variables that could influence the charging results; the "null hypothesis" was that the number of delivery robots was statistically independent of the charging results; then, a contingency table was compiled; the contingency table is... OK Column, theoretical number of times as follows: （1） in Given the sample size, then calculate the statistics. : （2） Based on the set confidence level, the degrees of freedom are found to be... The chi-square distribution critical value is compared with the statistical value. If the statistical value is large, the null hypothesis cannot be rejected, meaning that the feature data variable is statistically independent of the charging result. Similarly, the statistical independence of the charging scheduling data of all intelligent delivery robots from the charging result can be obtained, and then the feature data variables that can affect the charging result can be screened out. The charging scheduling data includes the number of delivery robots, the location distribution of delivery robots, the delivery timeliness of delivery robots, the remaining battery power of delivery robots, the delivery workload of delivery robots, and the number and location distribution of charging piles. The characteristic data variables include the number of delivery robots, the location distribution of delivery robots, the delivery timeliness of delivery robots, the remaining battery power of delivery robots, the delivery workload of delivery robots, and the number and location distribution of charging piles. Then, based on the feature data variables that affect the charging results, a dataset for building a distributed charging cost optimization model for intelligent delivery robots is constructed; feature data variables that do not affect the charging effect of intelligent delivery robots are effectively deleted, the learning speed of neural networks is accelerated, and the efficiency of building a distributed charging cost optimization model for intelligent delivery robots is improved. Step 1.3: For the dataset obtained in Step 1.2, construct a distributed charging cost optimization model for the intelligent delivery robot using an L-BPNN neural network; to make the distributed charging cost optimization model for the intelligent delivery robot more closely match the actual charging scheduling conditions of the intelligent delivery robot. An L-BPNN neural network with linear mapping relationship is selected to construct a distributed charging cost optimization model for intelligent delivery robots, so that the distributed charging cost optimization model for intelligent delivery robots is more in line with the actual charging scheduling conditions of intelligent delivery robots. The L-BPNN neural network structure adds a direct connection between the input layer and the output layer on the basis of BPNN, reflecting the linear and nonlinear relationship between the input and the output; This indicates the input information. Indicates a hidden layer. Indicates the output value. This represents the weights between the input layer and the hidden layer. This represents the weights between the hidden layer and the output layer. This represents the weights between the input and output layers; therefore, the expression for calculating the output of the L-BPNN hidden layer remains: （3） In the formula This represents the activation function of the hidden layer; the sigmoid function is commonly used. Indicates the number of neurons in the hidden layer. Indicates hidden layer bias; The expression for the corresponding output layer is: （4） In the formula Indicates the number of neurons in the output layer. Indicates the output layer bias; The prediction framework of the distributed charging cost optimization model for intelligent delivery robots based on L-BPNN also includes four parts: the establishment of network topology and the initialization of related parameters, the learning and training of L-BPNN, obtaining the optimal network parameters, and the prediction of the distributed charging cost optimization model for intelligent delivery robots. After using L-BPNN to establish an optimization model for the deployment of delivery robots, a constraint model and optimization indicators based on charging time and power as costs are established based on real-time information of feature variables. Real-time information on feature variables includes current task volume, delivery timeliness, and the number and location distribution of charging stations; the optimization sub-problems are defined as follows: （5） st and （6） st in, The charging time cost under scheduling, The cost of charging power under scheduling, For the current workload, For the remaining delivery time, To determine the distance to the charging station under the dispatching system. This represents the robot's maximum battery capacity. Step Two: Further refine the distributed charging cost model for intelligent delivery robots constructed in Step One by combining it with constraints based on actual conditions; use aggregate game theory to solve the optimization problem of the distributed charging cost model for intelligent delivery robots. Aggregate game theory effectively utilizes the non-cooperative nature and mutual influence among characteristic data variables to improve the accuracy and efficiency of charging scheduling for intelligent delivery robots; in the aggregate game process of intelligent delivery robot charging scheduling, a global guidance variable is introduced, and each delivery robot updates its own charging strategy simultaneously according to the global guidance variable, which significantly shortens the computation time required for the aggregate game process of intelligent delivery robot charging scheduling to reach Nash equilibrium, while avoiding deviation problems caused by each robot excessively pursuing low costs. The deviation problem includes robots charging frequently in order to reduce charging costs; Step 3: Based on the intelligent delivery robot charging scheduling aggregation game optimization results described in Step 2, the parameters of the L-BPNN neural network of the intelligent delivery robot distributed charging optimization model are iteratively optimized through a genetic algorithm to improve the prediction accuracy and efficiency of the intelligent delivery robot distributed charging optimization model. Then, based on game theory, high-precision and efficient planning of delivery robot charging scheduling is realized, so that the intelligent delivery robot resources can achieve optimal deployment under different working conditions.

2. The delivery robot charging scheduling method based on aggregation game theory as described in claim 1, characterized in that: The process also includes step four, which involves planning the distributed charging of intelligent delivery robots based on steps one through three, according to the distributed charging task conditions of the intelligent delivery robots. Under the conditions of numerous tasks, scarce key resources, and spatially separated and scattered task execution locations, the introduction of global guidance variables avoids deviations caused by each robot excessively pursuing low costs, thereby improving the accuracy and efficiency of delivery robot charging scheduling, extending charging life, and increasing resource utilization.

3. The charging scheduling method for delivery robots based on aggregation game theory as described in claim 1, characterized in that: The second step is implemented as follows: Step 2.1: Based on the distributed charging cost optimization model for the intelligent delivery robot obtained in Step 1, further improve the model by combining it with the constraints of the actual situation; First, the problem is further improved and optimized by combining the constraints based on the actual situation, so as to obtain a more suitable charging scheduling scheme. The constraints based on the actual situation include task frequency and battery remaining SOC index. Considering practical realities, delivery tasks generally operate within a relatively stable range. To better reflect actual working conditions, task frequency needs to be constrained. When a battery is completely depleted during use, it causes severe battery discharge, damaging the internal electrode plates. Therefore, each instance of excessive discharge damages the battery's internal electrode plates. Each recharge after severe battery discharge causes the charger's input current to accelerate, leading to excessively rapid reaction and overheating of the internal electrode plates, potentially causing deformation and detachment of the electrode material. This also affects the battery's normal charge storage capacity, directly shortening its lifespan. Furthermore, severe deformation and detachment of the internal electrode plates after complete discharge can cause premature false saturation during charging, resulting in short-lived charge. Therefore, to extend battery life, the remaining charge level during charging needs to be constrained. s.t. (7) Step 2.2: An aggregation game approach is used to solve the distributed charging cost model optimization problem for intelligent delivery robots. This effectively utilizes the non-cooperative nature and mutual influence among characteristic data variables to improve the accuracy and efficiency of charging scheduling for intelligent delivery robots. In the aggregation game process of intelligent delivery robot charging scheduling, a global guidance variable is introduced, and each delivery robot updates its own charging strategy simultaneously based on this global guidance variable. This significantly shortens the computation time required to reach Nash equilibrium in the aggregation game process of intelligent delivery robot charging scheduling, while avoiding deviation problems caused by each robot excessively pursuing low costs. The optimized result of the aggregation game for intelligent delivery robot charging scheduling is then output. The deviation problem includes robots frequently charging to reduce charging costs. Aggregation game theory requires establishing a game model, designing global guiding variables, and then solving for the Nash equilibrium strategy. Based on the battery characteristics of the delivery robot, the charging strategy, and the non-cooperative nature and mutual influence of different robots' power resource requirements, a cost function for the charging game is established. Multiplayer aggregation games are described using three basic elements: participants, strategy set, and cost function; Represents the set of tags for participants, using Indicates the first The set of strategies of each participant, and using Represent the decision variables of this participant; use Indicates the first The cost function of each participant, where （8） （9） They represent the exceptions All decision variables and all strategy combinations except The set For each , No. The goal of each participant is to address the current situation. Choose decision variables This makes the cost function To reach the minimum; furthermore, for convergent games, there is also a convergent mapping. Defined as （10） in Map local decision variables to aggregate terms; and the cost function satisfies... （11） （12） in , ; In addition, the average charging strategy of the delivery robot group is used as a global guiding variable, and each delivery robot updates its own charging strategy simultaneously based on the global guiding variable.

4. The delivery robot charging scheduling method based on aggregation game theory as described in claim 3, characterized in that: In step three, The optimization part of the genetic algorithm is the weights between the input layer and the hidden layer. and hidden layer bias Weights between hidden layers and output layers and output layer bias and the weights between the input and output layers. ; The neural network is used as the main function of the genetic algorithm, and the error function of the L-BPNN neural network is set as the fitness function; the population size is the number of effective samples. The fitness of a single individual is The probability of it being selected is: （13） After initial setup, crossover and mutation operations are performed to obtain offspring. Finally, the fitness of each individual is calculated to retain the optimal individual in each iteration, thereby optimizing the parameters of the L-BPNN neural network of the intelligent delivery robot distributed charging optimization model. This improves the prediction accuracy and efficiency of the intelligent delivery robot distributed charging optimization model, that is, it realizes high-precision and efficient planning of delivery robot charging scheduling based on game theory, so that the intelligent delivery robot resources can achieve optimal deployment under different working conditions.

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