Dynamic Scheduling and Optimization of AGV in Factory Logistics Systems Based on Digital Twin

Abstract

At present, discrete workshops demand higher transportation efficiency, but the traditional scheduling strategy of the logistics systems can no longer meet the requirements. In a transportation system with multiple automated guided vehicles (multi-AGVs), AGV path conflicts directly affect the efficiency and coordination of the whole system. At the same time, the uncertainty of the number and speed of AGVs will lead to excessive cost. To solve these problems, an AGVs Multi-Objective Dynamic Scheduling (AMODS) method is proposed which is based on the digital twin of the workshop. The digital twin of the workshop is built in the virtual space, and a two-way exchange and real-time control framework based on dynamic data is established. The digital twin system is adopted to exchange data in real time, create a real-time updated dynamic task list, determine the number of AGVs and the speed of AGVs under different working conditions, and effectively improve the efficiency of the logistics system. Compared with the traditional scheduling strategy, this paper is of practical significance for the scheduling of the discrete workshop logistics systems to improve the production efficiency, utilization rate of resources, and dynamic response capability.

1. Introduction

In recent years, with the rapid development of information technology, digital factories with few people or none at all are gradually replacing traditional factories. In the flexible workshop of digital factories, each equipment communicates with the information control system, and the flexible manufacturing system (FMS) and flexible transportation system (FTS) tend to be automated in a gradual fashion. AGVs play a crucial role in the workshop logistics system and have become an indispensable part of the transportation system [1,2,3]. The logistics system is characterized by poor stability but strong dynamics. In factories, a single AGV is far from able to meet the transportation demand, but the path planning of multiple AGVs is more complex than that of a single AGV, which is prone to causing congestion and conflicts [4]. Therefore, the AGVs dynamic scheduling strategy in the flexible job shop scheduling problem (FJSSP) is an NP (Non-deterministic Polynomial)-hard problem and is difficult to optimize. At the same time, dynamic interference in the workshop logistics system can lead to deviation between the actual production and plan. Dynamic scheduling is not only a real-time response to real data, but also a way to reschedule and adjust after uncontrollable emergencies [5]. Besides the transportation tasks, task attributes, AGV number, AGV speeds under different working conditions, and the AGV battery power condition are also key points for the logistics system in terms of improving efficiency.

Currently, the market has put forward more stringent requirements for manufacturing enterprises’ production efficiency, response speed, personalized response degree and energy consumption reduction, which has presented new challenges for enterprises to participate in market competition. The traditional informatization has improved the production efficiency of enterprises, but it lacks the deep embedding of the production system, and the traditional informatization idea in particular has not realized the intelligent transformation of the logistics system. Therefore, enterprises respond to market changes quickly and effectively through intelligent manufacturing, the timely adjustment of production capacity, and transportation mode. The objective is to satisfy customers’ expectations and needs through lower manufacturing costs. Few researchers consider multi-AGVS and multi-objective scheduling rules, task allocation and reasonable allocation of AGVs resources at the same time. Dynamic scheduling mainly focuses on shop scheduling through real-time or offline production data, which means dynamic scheduling based on the connection between the digital world and the physical world. The complex environment and dynamic tasks in the discrete logistics system make it difficult to exchange data quickly. As a result, the digital space cannot obtain the data from the physical space in real time, and the adjusted scheduling plan cannot be carried out as expected. Therefore, data exchange between the digital space and physical space is the key to realizing AGVs multi-objective dynamic scheduling. In recent years, digital twin technology has become the research focus for institutions, scholars and enterprises. As one of the most authoritative research and consulting companies, Gartner has listed the digital twin as one of the top ten strategic technology development trends [6]. Digital twin provides an idea and framework to solve the aforementioned problems.

1.1. Contribution

An AGVs multi-objective dynamic scheduling method (AMODS) for a factory logistics system is presented based on the digital twin in this paper. A virtual digital twin with high fidelity is constructed to provide a visual simulation platform for the verification of mechanical action, control logic, operation scheme of the production unit and the dynamic scheduling scheme in the physical world. A framework is set up to analyze the dynamic data and control mechanism of two-way interactions. A real-time updated dynamic task list is constructed to realize the dynamic scheduling of multi-objective routes for AGVs. The optimal number of AGVs and the speed optimization of AGVS under different working conditions are analyzed. In this study, a real logistics production line is chosen to verify the proposed methods.

1.2. Paper Organization

The remainder of this paper is organized as follows. The Section 2 describes the related work. The Section 3 discusses the logistics job-shop scheduling framework based on the digital twin. The Section 4 presents the virtual digital twin of high fidelity. The Section 5 formulates the problem of AGV scheduling. The Section 6 introduces the AMODS method for complex discrete logistics systems. Section 7 analyzes a practical case. Section 8 provides some conclusions.

2. Related Works

In a logistics system, the path planning and scheduling strategy of AGV is the core of the whole system, and the quality of the scheduling algorithm can directly affect the balance and stability of the system. Multi-AGV path planning has always been a hot research topic, and many researchers have improved the scheduling strategy of AGVs. Hu et al. [7] considered the constraints of transportation time and transportation resources in the flexible job shop and proposed an improved local search algorithm combining greedy heuristic rules. Sahu et al. [8] proposed a hybrid algorithm of democratic robotics PSO and improved Q-learning, and found that it is fast and available for a real-time environment. Saeed et al. [9] studied the multi-objective path planning problem and found the shortest collision-free path connecting a set of given target points in the robot’s working environment. Zhang et al. [10] proposed a dynamic scheduling method for self-organizing AGVs in a logistics system. Dynamic scheduling rules are learned by using improved gene expression programming and cooperate with other AGVs for transportation. Zhong et al. [11] realized integrated scheduling and conflict-free path planning for multiple AGVs. By establishing a mixed integer programming model and using hybrid genetic algorithm-particle swarm optimization (HGA-PSO), AGV path conflict or deadlock is avoided. Hu et al. [12] proposed a new variable neighborhood search algorithm for the conflict-free scheduling of large-scale multi-load AGVs. The retention time table is used to prevent collisions and deadlocks between multiple AGVs, which can achieve the scheduling of multiple AGVs in a large and dense network. Wang et al. [13] proposed a new multi-state scheduling algorithm (MSSA) to make use of idle AGVs. Xu et al. [14] took minimizing the completion time as the goal, analyzed the load time and no-load time of each station, and proposed an improved gray wolf algorithm to optimize the scheduling of AGVs in a flexible job-shop.

In addition to the design of AGVs scheduling strategy, most flexible job-shop logistics systems are based on the premise of multi-target objects. In view of the attributes of AGVs itself, Chen et al. [15] proposed a multi-AGVs efficient routing combining centralized control and decentralized control. Centralized control optimized the AGV path nodes, while decentralized control adjusted the AGV speed. Gao et al. [16] proposed a throughput evaluation methodology based on AGV route decomposition that is proposed for AGV transportation systems. AGV speed change and collision avoidance are considered, as well as the promotion of the productivity of AGV transportation system. Zou et al. [17] proposed an efficient Multi-Objective Greed Algorithm (MOGA). The algorithm has effective strategies such as new population initialization, greedy operation, and an adaptive multi-domain local search, and optimizes the energy consumption of AGVs and the number of AGVs.

For the adaptability of the scheduling system to the real environment, the application of dynamic scheduling in the actual discrete shop floor has always been a difficult problem. Liu et al. [18] constructed the mathematical model of flexible multi-objective dynamic scheduling of the shop floor and proposed a multi-objective flexible dynamic scheduling algorithm based on an adaptive genetic algorithm. Zhang et al. [19] combined a dynamic interaction layer and particle swarm genetic hybrid algorithm to realize the dynamic scheduling of urgent tasks in view of the dynamic disturbance in flexible job shop scheduling. For the urgent orders for small batch production tasks, Liu et al. [20] proposed a double-loop deep Q network based on a perception-cognition dual system to minimize the average load of equipment and to minimize the total completion time.

In reality, the power of AGVs is limited, and working for a period of time will consume the battery power. Many researchers have studied the problem of pre-sensing energy consumption data acquisition in the case of limited battery capacity. Gul et al. [21] discussed the importance of energy sensing data collection for robots and wireless sensor networks, and researched the collection of energy sensing data in the robot network cluster, including the remaining battery capacity of UAV (Unmanned Aerial Vehicle). Gul et al. [22] studied the problem of energy saving data collection and considered the data collection of limited capacity battery UAV to carry out path planning and the minimization of the total energy consumption of UAV and record the data of the lowest cost. Han et al. [23] proposed an AGV dynamic scheduling method based on digital twins. The problem of AGV charging in an AGV scheduling system is solved by using the characteristics of virtual reality interactive data and fusion in digital twinning technology, and the operation efficiency of the workshop is effectively improved.

Digital twin technology is designed to create a virtual model of a physical entity in a digital way, to simulate the behavior of a physical entity in the real environment with the help of data, and to expand new capabilities for the physical entity by interactions between digital space and physical space, data fusion, and decision iterative optimization. It is oriented to the whole product life cycle and plays the role of bridge and link between the physical world and the digital world, to achieve digitization, intelligence and the networking of the factories. Many scholars have researched the construction, data collection and monitoring of digital twins. Tao et al. [24] proposed the concept of the digital twin workshop, described the system composition, principal mechanism, characteristics and key technologies of a digital twin workshop, and further discussed the theory and implementation methods of the interaction and integration between physical space and digital space based on workshop data. Dahman et al. [25] proposed a simulation framework based on testable digital twins and virtual test platforms, combining the latest virtual reality and 3D simulation technology. Tao et al. [26] proposed a dynamic scheduling method for the discrete assembly shop of complex products based on digital twin to realize data interactive dynamic scheduling between physical space and digital space. Mahesh et al. [27] has developed a digital twin framework to improve productivity through bottleneck analysis, process mining and diagnostic analysis.

3. Logistics Scheduling Framework Based on Digital Twin

The mapping and real-time interaction of digital twins are used to realize the dynamic data exchange and integration between the physical world and the digital world of the workshop, which can greatly improve efficiency.

3.1. Architecture of Digital Twin for Workshop Logistics System

The dynamic scheduling architecture of a workshop logistics system based on digital twin is composed of the physical world, virtual world, digital twin engine and service management system, as shown in Figure 1. The physical world means the intelligent hardware devices, such as sensors, PLC (Programmable Logic Controller), RFID (Radio Frequency Identification) tags and RFID readers. The motion logic and performance of the physical world lays a foundation for the digital twin in the virtual world. At the same time, data acquisition tools can transmit real-time dynamic data to the digital twin engine. The physical world is the basis for the digital twin system, and it is also the ultimate target to be optimized for the digital twin system. The virtual world is composed of digital models and information systems. It is the virtual mapping of the physical world and synchronizes the data and models of the physical world. The virtual world provides the model and data for the digital twin engine, and receives data feedback from the digital twin engine. The digital twin engine is the engine to realize the real-time connection between virtual and real space, and it is also the core of the whole digital twin system. It is composed of an interactive drive, data storage and management, model management, an intelligent scheduling algorithm, a historical knowledge database and a communications system. The interactive drive connects the physical world, virtual world and the interactive interface of the service management system. Data management needs to be integrated with model management before intelligent computing analysis. The historical knowledge database contains the optimization data and theoretical data of basic algorithms recorded in previous historical iterations. The communication system is composed of a Web Service, database interface, a TCP/UDP (Transport Control Protocol/User Data Protocol), and an OPC UA (Object Linking and Embedding for Process Control Unified Architecture). The communication between the physical world, virtual world and service management system can be realized through the communication system. The service management system generally includes the WMS (Warehouse Management System), SCM (Supply Chain Management), MES (Manufacturing Execution System), RRP (Recommended Retail Price) and PDM (Product Data Management), which can realize the visual analysis of data, the scheduling of production plans and the management of the digital twin system. The visual data will be fed back to the physical world workshop and the virtual world workshop synchronously in real time and will also be recorded in the digital twin engine.

3.2. Functional Logic of the Workshop Digital Twin System

The functional logic of the workshop digital twin system is shown in Figure 2. The model simulation module is a 1:1 real restoration of the entire workshop logistics system; it lays the foundation to map the physical world in the digital twin of the logistics system. The real-time monitoring module monitors the physical workshop and its digital twin, collects and updates data synchronously, and visualizes relevant data. The intelligent control module can control the physical workshop and its digital twin when receiving relevant signals. It can also feedback the prediction results to the device based on the local/cloud database. The forecasting and monitoring module can predict and judge the future change trend by accumulating data, and analyze the charging situation of AGVs, equipment failure, and product market supply and demand. The data acquisition module collects the relevant data in the physical workshop through the commonly used data acquisition tools in the factory. The background analysis module can check the adaptability and reliability of the digital twin system by collecting real-time prediction, data from the physical workshop, and its digital twin for comparative analysis and generating an error/time difference analysis report.

4. Construction of Digital Twin

There are usually two steps to construct the digital twin of a factory. The first step is to use a stereoscopic virtual action model to simulate the factories. The model is drawn at equal scale through three-dimensional software, or the virtual model is obtained with the help of a 3D (3 Dimensions) modeling scanner. The stereo models are light weighted, and then the motion joint is bonded with signals to achieve the interactions. The second step is to build a model for production simulation and analysis. The model reflects the logic of the production process, and carries out simulation analysis, calculation and verification on the scheduling strategy of the production process.

4.1. Construction of Virtual Action Model

Mechanical equipment in industrial workshops is usually very complex. In the process of 3D modeling, high precision models generally have multiple geometric faces. A large amount of computer memory is occupied. Therefore, it is necessary to light weight the models, simplifying the unnecessary structure. For example, the chamfers, fillets, redundant points, lines and surfaces are removed, and the non-moving parts should be combined into one component. Finally, the light weighted models are imported into the virtual engine platform for rendering, physical characteristics and behavioral logic are added, and relevant signals are configured.

In this section, only AGVs and single stations are taken as examples. As shown in Figure 3, the light weighted AGV and workstations are imported into the virtual engine platform. The operation logic and collision sensing device of AGV and station are added, and the sensing signal and data interface are configured. Socket communication based on a TCP/UDP protocol is used in the platform, which transmits the collected data of the physical equipment to its digital twin through the network port and matches the relevant signals.

4.2. Model Establishment for Production Simulation Analysis

The production simulation analysis models are often used for discrete event simulation. Pre- production can be carried out on this model before the actual logistics system runs, and the scheduling strategy can be simulated and verified in advance. The production simulation and analysis models have no high requirements on the appearance and action effect restoration of the equipment model. Its core feature is to reflect the operation logic of the whole production line or the whole workshop. The data are processed and analyzed, and the algorithms are verified and optimized, in order to greatly reduce resource consumption and improve production efficiency.

In this section, only AGVs and single stations are taken as an example. The software used to build the simulation analysis model is Plant Simulation. As shown in Figure 4, the model can be divided into four modules: a simulation module, control module, analysis module and communication module. The simulation module simulates the production process of the actual workshop production line. The control module is responsible for the optimal control of the scheduling algorithm, production scheduling, and path planning during transportation. The analysis module generates the corresponding analysis report chart during the simulation to prove the applicability of the transportation plans and scheduling algorithms. The data is stored in MySQL (My Structured Query Language) database for reference of the service management system. The communication module provides many interfaces for dynamic interaction between simulation models and physical plants, such as OPC UA, PLCSIM, ODBC (Open Database Connectivity), SQL and Socket. At the same time, the production simulation analysis models are integrated with MES, WMS and Excel to obtain real-time logistics data, form dynamic reports, and feedback the status of the production line in a timely and visual manner.

4.3. Interaction between the Digital Twin and Physical Equipment

In the digital twin system, both data and model are indispensable. The virtual action model provides a high-fidelity animation model, which can restore the entire logistics system. However, the virtual action model needs to be matched with the physical device and complete the virtual action through an external data drive. The implementation of the data drive can generally be divided into two types. The first one is the data driving of the actual workshop communication interface, and the other one is the data from the external simulation analysis software. The simulation analysis model plays an important role in the production process simulation, algorithm verification and data analysis capabilities. At the same time, it is combined with the service management system to obtain real-time logistics data, generate dynamic reports, and verify and predict future trends of the logistics system in advance.

A high fidelity digital twin receives data from a physical device and evolves in real time, so it keeps consistent contact with physical device objects throughout their life cycle. To ensure real-time data exchange in a digital twin system, the interaction between a virtual action model, simulation analysis model and a physical device should be established as shown in Figure 5. The virtual action model and the simulation analysis model communicates via the TCP protocol. The IOT (Internet of Things) equipment in the physical workshop acquires PLC/sensor data and uploads it in JSON (JavaScript Object Notation) format in real time. The digital twin then acquires the data from the server in real time through socket communication. Physical devices communicate with the digital twin in real time as well. At present, the common PLC/sensor supported communication protocols in intelligent factories include OPC UA and Modbus. At the same time, a communication converter is required between different communication protocols. In the data exchange among the virtual action model, simulation analysis model and physical equipment, data input and output logic can be divided into the physical workshop server driver and the simulation analysis model server driver. The physical workshop server driver drives the virtual action model and the simulation analysis model with the data collected from the real physical workshop. The simulation analysis model server driver is used to optimize the simulation based on the received service management system data or the corresponding transportation route, and drive the virtual action model and physical equipment. The simulation analysis model server driver focuses on pre-validation, algorithm analysis and demand forecasting.

5. Problem Formulation

In the workshop logistics systems, the customers place an order in the remote service management system. The order is scheduled and distributed to the production line. The AGVs in the empty state receive the new task in real time, go to the task point to load the cargo, transport the cargo to the designated destination, unload them, and then continue to receive new tasks. The initial position of AGVs is the default starting point, and the initial state of AGV is a no-load state. If no new task information is received after the current task is completed, the AGV completing the task will stay at the current point. When the AGV power is lower than 25%, it goes to the nearby charging area for charging. By combining the characteristics of the digital twin system, the real-time dynamic data exchange between the real production line and the virtual digital twin is established, and the dynamic scheduling strategy and AGV attribute configuration are verified and predicted. Finally, the method is implemented on the real production line. In this study, there are several important assumptions and constraints:

1.

The distribution capacity and scope of each AGV are the same, and all AGVs are the same;

2.

An AGV can only load and distribute one cargo each time;

3.

The task allocation rule is on a first come, first serve basis [28] (FCFS);

4.

AGVs adopt the shortest path;

5.

The failure of AGVs should be considered; the availability of the AGVs is 95%, and the mean time to repair (MTTR) is 5;

6.

The transportation track can only allow one AGV to pass without overtaking, and there should be a safe distance between any two AGVs;

7.

AGVs have different speeds under load and no load, which lies in ranges;

V_Lmin < V_L < V_Lmax,

(1)

V_ULmin < V_UL < V_ULmax,

(2)

8.

The loading and unloading time of AGVs should be considered;

9.

An AGV cannot go to the charging area during transportation.

6. AMODS Method for Complex Discrete Logistics System

The framework and action communication logic of the AMODS method have been presented in Section 3 and Section 4. The framework and action communication logic are the theoretical basis of the AMODS method. This method introduces the real virtual dynamic interaction process. Aimed at the scheduling the optimization problem in the logistics system, the intelligent algorithm of the AMODS method is used to plan the path of AGVs and search for dynamic scheduling optimization in the logistics system. Among them, intelligent algorithms include order scheduling, AGV task scheduling and AGV path planning. The AMODS method can also predict the demand for real-time resources. This method, mainly realizes the verification and interaction of equipment action, control logic, AGVS path planning and the dynamic scheduling strategy between real transportation production lines and the virtual digital twin. It provides an intelligent scheduling method for the logistics system, covering the whole life cycle of the transportation process. The order is visualized and accurately positioned to facilitate after-sales inquiry. The transportation efficiency and convenience have been improved greatly. The AGVs multi-objective dynamic scheduling (AMODS) method in this paper is implemented in the speaker assembly line of a discrete manufacturing workshop.

6.1. The Process of AMODS Method

The AMODS method based on the digital twin is shown in Figure 6. The MES system exchanges data with the digital twin of the logistics system, and the data can be recorded and displayed through the visualization platform. Customers send orders through the APP(application). When receiving the new order, the virtual twin production line generates a preliminary scheduling plan according to the original scheduling strategy in the historical knowledge database and feeds it back to the real transportation production line. When the real production line executes the preliminary scheduling plan, the data acquisition center and the decision control center also synchronously send real-time data to the virtual twin production line. When there are multiple dynamic tasks and empty AGVs in the logistics system, it is necessary to determine the routing of the tasks and AGVs. Therefore, the pending orders and transportation loading and unloading signals in the virtual twin production line are dynamically written into the dynamic task list. According to the scheduling of the dynamic task list, empty AGV is scheduled first, and then, based on the principle of zero conflict and shortest path, AGV transportation path planning is carried out, and the optimized scheduling plan is fed back to the real transportation production line. If the scheduling plan does not meet the requirements, the intelligent algorithm scheduling needs to be triggered again.

6.2. Design of Intelligent Algorithm

The intelligent algorithm of the AMODS method is adopted for path planning and dynamic scheduling optimization of AGVs in the logistics system. The assignment of AGVs tasks is completed by updating the dynamic task list in real time. The route from the starting point to the target point of AGVs is found according to the shortest path principle. Because the AGV is expensive, it is necessary to determine the rational number of AGVs. Predicting and optimizing the number of AGVs and the speed under different working conditions through the virtual twin production line can improve the productivity and production efficiency, making full use of the AGVs.

6.2.1. Scheduling Principle of Dynamic Task List

The dynamic task list consists of order scheduling and the loading/unloading signal. Both will assign transportation tasks to AGVs. The loading/unloading signal is the signal sent by each processing station. When a station completes the current processing step, an AGV needs to transport the cargo to the next station for processing. Orders issued by customers are scheduled through MES. Order scheduling can reasonably allocate coefficients according to the customer classification principle, order priority principle, process flow principle and order placement time principle, and the order scheduling sequence obtained is written into the dynamic task list. The order scheduling is shown in Figure 7. The customer priority, order priority, order placement time and process complexity level need to be normalized, and the data is mapped to 0–1 by changing the original data.

6.2.2. Algorithm Process

The intelligent algorithm in the virtual twin production line performs path planning and dynamic scheduling optimization for AGVs in the logistics system, as shown in Figure 8. New tasks are written to the dynamic task list in real time through MES scheduling and loading/unloading signals. The dynamic task list accumulates records from top to bottom. The tasks schedule the no-load AGV according to the principle of first come first serve. The task to be allocated is recorded through the global variable. When receiving the new task, the path with the shortest path and no conflict [29] is found based on the Dijkstra algorithm. The unloaded AGV goes to the starting point to transport the cargo to the target point according to the path. When the AGV is in the no-load state, it is necessary to detect the battery usage of the AGV. Because 25% of the power is enough to complete any transportation task, when the power is lower than 25%, the AGV needs to go to the nearby AGV charging area.

6.2.3. Determination of the AGVs Attributes

When the production line in the workshop is started, a large amount of real-time data will be generated. The digital twin continuously analyzes the real-time data and historical data from the real transportation production line and virtual twin production line. In this way, the demand of the production line is predicted, the scheduling plan is generated, and the attributes of the AGVs are optimized through multi-level experiments in the virtual twin production line. The final target is to make full use of the logistics system, improve the transportation efficiency, and save costs.

7. Case Study

To verify the proposed AMODS method based on digital twin, a case study is conducted on an assembly line in a discrete manufacturing workshop in order to realize the real-time interaction between the virtual workshop and the physical workshop, AGVs dynamic scheduling, and AGV attribute optimization.

7.1. Case Description

The layout diagram of the assembly line is shown in Figure 9. It has five stations (material source station, speaker body and base assembly station, marking station, packaging station, warehouse station) and two AGV charging areas. There are three different raw materials to be assembled in the material source station. A buffer area is set beside each station. The AGV pool is the starting point of the AGV. The material source station generates raw materials to be assembled according to the order from the client APP. AGV transports different raw materials to different stations for processing. When the assembly work is completed at a station, the AGVs need to transport the processed products to the next station for processing. When all the assembly work is completed, the finished products are transported to the warehouse by AGVs. When the AGV power is lower than 25%, the AGV goes to the nearby charging area for charging. The symbols of each station in the simulation model are shown in

Table 1. Machining time of each station and the meaning of symbols.

Symbol	Production/Processing Time	Meaning
Source	30 s	Material source workstation
Store	3 s	Material source buffer area
S1	20 s	Chassis-Loudspeaker box assembly station
S2	10 s	Marking station
S3	20 s	Packing station
Charging_area	15 min	AGV charging area
M_End	/	Material Ending
M1	3 s	Chassis buffer area
M2	3 s	Chassis-Loudspeaker box buffer area
M3	3 s	Loudspeaker box buffer area
M4	3 s	Unmarked buffer area
M5	3 s	Marked buffer area
M6	3 s	Packing box buffer area
M7	3 s	Finished product buffer area
M8	3 s	To be packed Chassis-Loudspeaker box buffer area
M9	3 s	Warehouse buffer area
AGV_LoadingTime	5 s	AGV loading time
AGV_UnLoadTime	5 s	AGV unloading time

, and the corresponding destinations of raw materials are shown in

Table 2. The processing station corresponding to the raw material to be processed.

Materials	Location	Destination
Loudspeaker box	Store	M3
Packing box	Store	M6
Chassis	Store	M1
Chassis-Loudspeaker box	M2	M4
Marked Chassis-Loudspeaker box	M5	M8
Finished product	M7	M9

:

7.2. The Virtual Twin Model of an Assembly Line

The virtual twin model is built for the real assembly line, including the simulation analysis model and the virtual action model. The simulation analysis model is shown in Figure 10, which contains many functional tools. The symbols of each function module in the simulation analysis model are shown in

Table 3. The symbols and meanings of the simulation analysis model.

Symbol	Meaning
Start_point	The global variable of start points
Target_point	The global variable of target points
Finished_products	The global variable of finished product quantity
Load_speed	The global variable of the AGV load speed
Unload_speed	The global variable of the AGV unload speed
Ran/Seq_prod_table	Raw material list
AGV_Task	AGV task list
Shift_Calendar	Workshop shift calendar
Ganntt_Chart	Gantt chart of station state
M	Relevant control procedures

. The virtual action model is shown in Figure 11.

7.3. Simulation Data Modeling and Implementation

The virtual twin model of the assembly line interacts with the real-time data of the real production line. In the model, static data such as equipment failure rate and mean time to repair are loaded firstly. Each action event is coded with signals, and in the virtual twin model trigger signals are set for each object. Through the communication protocol, event signals are associated with model object signals. The equipment data and production task data generated in real time can be used to build a data model as shown in Figure 12. The data is classified and stored to facilitate the direct use in the simulation process. In this case, the assembly line based on the digital twin system reads data from the database at a time interval of 100 ms, realizing the restoration of the real production line and visual real-time monitoring.

7.4. The Real-Time Dynamic Task List

The pseudo code of the loading program is shown in

Table 4. Pseudo code of the loading program.

1    AGV.Stopped = true

2    wait TL

3    if AGV.cont.empty then

4      Material.move(AGV)

5    end

6    AGV.destination = Destination.point

7    AGV.speed = VL

8    AGV.Stopped = false

. Here, T_L is the loading time of the AGVs, cont is the capacity of AGV, Material is the transportation objects, destination is the target point of AGV, and Destination.point is the target point recorded by global variables.

The pseudo code of the unloading program is shown in

Table 5. Pseudo code of the unloading program.

1    AGV.Stopped = true

2    wait TUL

3    while AGV.cont.num > 0

4      AGV.cont.move(Mj)

5    end

6    waituntil AGV_Task.yDim > 0

7    Start_point == AGV_Task[1,1]

8    Destination_point == AGV_Task[2,1]

9    AGV_Task.cutRow(1)

10     AGV.speed = VUL

11     AGV.Stopped = false

. Here, T_UL is the unloading time of the AGVs, M_j is the station of number j, AGV_Task is the AGV dynamic task list, and cutRow is the order to delete a row in the AGV dynamic task list.

The dynamic task list is shown in Figure 13. The first column in the list is the task starting point, and the second column is the corresponding target point. The list shows the tasks that have not been executed yet.

The traditional scheduling is that the raw materials are transported to S1 by AGVs, and then to S2 after the assembly of S1. After several station processing, the finished product is transported from AGV to M_End. When an AGV completes a finished product, it will continue with the next task. The Gantt chart of the traditional scheduling is shown in Figure 14a. The scheduling based on the dynamic task list is that AGV transportation tasks are recorded in the dynamic task list in real time. The dynamic task list accumulates records from top to bottom. Once there are tasks in the dynamic task list, the tasks schedule the no-load AGV according to the principle of first come first serve. The AGV receiving the task assignment goes to the task point according to the shortest path principle. AGV is called through the dynamic task list, which improves the utilization of AGV and reduces the waiting time of AGV. The Gantt chart of the real-time dynamic task list scheduling is shown in Figure 14b. As shown in Figure 14, the time cost of the traditional scheduling is about 12 min, while the time cost of the real-time dynamic task list scheduling is about 10 min, which is 16.7% shorter than the traditional scheduling.

7.5. Optimization of the AGVs Attributes

The number and the speed of AGVs are optimized through multi-level experiments. The input and output variables of the experiments are shown in

Table 6. Experiment input variables.

Input Variables	Description
root.AGVpoor.number	The number of AGVs
root.load	Speed of AGV load
root.UnLoad	Speed of AGV unloaded

and

Table 7. Experiment output variables.

Output variables	Description
root.M_end.StatThroughputPerHour	Material ending throughput per hour
root.M_end.StatAvgLifeSpan	Average life of the material
root.M_end.StatNumIn	Material final output

, and the value-added definition of multi-level experiments is shown in

Table 8. Value-added definition of multilevel experiments.

Attribute	Input	root.AGVpoor.number	root.load	root.Unload
L	Lower limit	1	0.5	1
U	Upper limit	10	1	2
A	Increment	1	0.1	0.1

. The input value should be within the appropriate range. If the number of AGVs, AGV load speed and AGV no-load speed are taken as inputs at the same time during the experiments, 660 rounds of experiments are needed, which will lead to a long analysis time. Therefore, this paper adopts a split multi-level experiment design. Firstly, an input variable is considered, and then the second variable is considered based on the optimized result of the former one. In this way, 39 rounds of experiments are required. The simulation time is 8 h.

As shown in

Table 9. Multi-level experiments for AGV quantity.

	The Number of AGVs/--	Material Ending Throughput Per Hour/(B/h)	Average Life of the Material/(hh:mm.ss)	Material Final Output /--
Exp 01	1	23.25	22:49.9469	186
Exp 02	2	39.5	5:27.8198	316
Exp 03	3	39.625	3:23.9833	317
Exp 04	4	39.625	4:12.2104	317
Exp 05	5	39.5	4:53.9322	316
Exp 06	6	39.5	5:16.0975	316
Exp 07	7	39.5	5:11.6064	316
Exp 08	8	39.375	5:29.3940	315
Exp 09	9	39.375	6:13.2387	315
Exp 10	10	39.5	5:37.6113	316

, when the AGV number is more than three, the material ending throughput per hour, the average life of the material, and the material final output will not be optimized further, which indicates that the saturation quantity of the AGVs is three.

As shown in

Table 10. Multi-level experiments for AGV number and load speed.

	The Number of AGVs/(--)	Speed of AGV Load/(m/s)	Material Ending Throughput Per Hour/(B/h)	Average Life of the Material/(hh:mm.ss)	Material Final Output/(--)
Exp 01	2	0.5	39.5	5:52.1321	316
Exp 02	2	0.6	39.5	5:34.5843	316
Exp 03	2	0.7	39.5	5:28.7617	316
Exp 04	2	0.8	39.5	5:27.8198	316
Exp 05	2	0.9	39.5	5:16.2430	316
Exp 06	2	1	39.5	5:16.5312	316
Exp 07	3	0.5	39.375	6:21.1874	315
Exp 08	3	0.6	39.625	3:44.9595	317
Exp 09	3	0.7	39.625	3:45.5663	317
Exp 10	3	0.8	39.625	3:23.9833	317
Exp 11	3	0.9	39.625	3:34.5650	317
Exp 12	3	1	39.625	3:33.9485	317
Exp 13	4	0.5	39.5	5:50.7031	316
Exp 14	4	0.6	39.625	4:21.4170	317
Exp 15	4	0.7	39.625	4:19.3005	317
Exp 16	4	0.8	39.625	4:12.2104	317
Exp 17	4	0.9	39.625	4:11.2851	317
Exp 18	4	1	39.625	4:10.5101	317

, the number of AGVs changes slightly around its saturation quantity, and multi-level experiments of the load speeds are conducted to find the optimal value of the load speed. As shown in

Table 11. Multi-level experiments for unloaded speed.

	Speed of AGV Unloaded /(m/s)	Material Ending Throughput Per Hour/(B/h)	Average Life of the Material /(hh:mm.ss)	Material Final Output/(--)
Exp 01	1	39.625	4:22.8332	317
Exp 02	1.1	39.625	4:22.0538	317
Exp 03	1.2	39.625	4:11.8165	317
Exp 04	1.3	39.625	4:09.8689	317
Exp 05	1.4	39.625	4:08.2005	317
Exp 06	1.5	39.625	4:06.8371	317
Exp 07	1.6	39.625	4:12.5574	317
Exp 08	1.7	39.625	4:11.9212	317
Exp 09	1.8	39.625	4:11.3588	317
Exp 10	1.9	39.625	4:10.8556	317
Exp 11	2	39.625	4:10.5101	317

, the optimal value of no-load speed can be found. Through the multi-level experiments, it is found that the production efficiency of the production line is optimized when the number of AGV is 3, the AGV load speed is 0.8 m/s, and the AGV no-load speed is 1.5 m/s. The optimized performance of the production line is shown in

Table 12. Optimized performance of the production line.

Simulation Time: 8:00:00.0000
Cumulative Statistics of Finished Products
Object	Name	Average Life of the Material	Throughput Capacity	TPH	Production	Transportation	Storage	Value Has Been Added	Distribution
M_End	Finish products	03:10.7	317	40	47.21%	15.56%	37.23%	10.49%

.

8. Conclusions

In this paper, an AGVs multi-objective dynamic scheduling method (AMODS) based on digital twins in a factory logistics system is proposed. The proposed AMODS method is applied to the AGV dynamic scheduling problem of a digital twin system, and an application example is given. The main conclusions are as follows:

• In the traditional factory logistics system, the data of information space and physical space lack integration and interaction, and the whole process elements in the transportation process have low predictability, linkage and global optimization level. The scheduling framework based on digital twins is built, and the virtual digital twin is constructed to map the physical logistics system with data and model. Through the combination of data and model, the interaction of a virtual action model, simulation analysis model and physical equipment is achieved.
• The real-time updated dynamic task list is introduced to generate a scheduling plan according to the actual production line demand. An AGVs multi-objective dynamic scheduling (AMODS) method based on digital twins was designed. The test results indicate that the time cost of the traditional scheduling is about 12 min, while the time cost of the real-time dynamic task list scheduling is about 10 min, which is 16.7% shorter than the traditional scheduling. The advantages of this method are verified and the transportation efficiency is improved.
• The AGVs attributes are optimized with multi-level experiments. Through the case study, it proves the feasibility and good scheduling performance of the production line with the help of the AGVs multi-objective dynamic scheduling method (AMODS) based on the digital twin. The experimental results show that the optimal number of AGVs is three, the optimal no-load speed of AGVs is 1.5 m/s, and the optimal load speed of AGVs is 0.8 m/s.

This provides a new solution for AGVs scheduling in a workshop logistics system. Based on the dynamic data exchange and fusion of the digital twin system, it can realize the synchronization of the digital and physical workshop and the demand prediction and optimal utilization of resources. However, the dynamic intelligent algorithm and predictive demand analysis studied in this paper are not comprehensive. Furthermore, it only considers the simulation development of the production line by understanding the working characteristics. At the same time, the production line layout and AGV routes of this study case are relatively simple, while the actual shop floor layouts are more complex. In the future, the scheduling and optimization based on artificial intelligent algorithms, AGV fault prediction and AGV power consumption prediction still need to studied further. They also need to act on a real workshop scene with a complex layout.