1. Introduction

Use of industrial mobile robots is becoming more and more common in modern manufacturing systems, especially in factories with island production cells that meet Industry 4.0 requirements. The mobile robot is usually seen as a serving unit, a device for material handling. In this article, we outline an approach where the mobile robot is the central element and the transport tasks are described in a much simpler way compared to previous models.

The study is motivated by the increasing trend of mobile robots and the fact that the selection of mobile robots to be integrated into manufacturing systems is simulation based and very time-consuming. The aim is to construct a simple model that describes the manufacturing system from the perspective of the mobile robot and thus can be rapidly calculated and the results obtained quickly. The article describes a theory concept, enhanced by a practical case study.

Industrial mobile robots are available from a wide range of manufacturers. Some companies specialize only in this area, larger players usually include these devices in their product range through acquisitions. The range varies from smaller or simpler automated guided vehicle (AGV) robots to more complex, intelligent mobile platforms with higher payloads (Oyekanlu et al., Reference Oyekanlu, Smith, Thomas, Mulroy, Hitesh, Ramsey, Kuhn, Mcghinnis, Buonavita, Looper, Ng, Ng’oma, Liu, Mcbride, Shultz, Cerasi and Sun2020).

An AGV, also known as an autonomous mobile robot (AMR), is a mobile platform that navigates along a predetermined path by means of a wire, painted or glued strip, or magnetic tape embedded in the floor (Hines, Reference Hines2021). Other solutions are also available using radio waves, lasers, or built-in image recognition systems for automated path planning. They are widely used in industrial installations and warehouses for moving heavy loads. Their application almost exploded at the end of the 20th century. Some of them carry loads that can be anything from raw materials to finished products, while others pull these in cargoes. These devices are also known by other names: the laser-guided vehicle (LGV), or the cheaper versions: automated guided carts (AGC). The term AMR is widely used nowadays to refer to vehicles that do not require external navigation infrastructure (wire in the floor). The short article from Hines also mentions the possibility of manual or automatic battery exchange as a possible direction for operational reliability.

AGVs were first introduced in 1955 and since then they have developed massively (Fazlollahtabar and Saidi-Mehrabad, Reference Fazlollahtabar and Saidi-Mehrabad2015). Their applications and types have grown and are still growing significantly. There are both outdoor and indoor applications, including in manufacturing, distribution, package delivery, wherever patterns can be used to organize the transportation work. According to a 2000 publication (on the research mentioned in the article of Saidi—Mehrabad) 20,000 units AGVs were used in industry. Adding to the 2015 figure, the increase is significant, as the International Federation of Robotics report for 2024 shows a 35% increase in the number of transport and logistics robots, with 1,13,000 units in 2023. The differences between the old and the newer types of AGVs concern the number of AGVs, the number of transport tasks, the degree of utilization of AGVs, the distance travelled, and the number of pick-up and delivery points. Development of new analytical and simulation models is needed that can overcome the huge computational time requirements, deadlocks, system latencies, and limited design horizons due to NP-hard problems (problems that cannot be solved in polynomial time).

There have been many studies on energizing mobile robots, of more than 140 in total by Muhammad and his coresearchers (Farooq et al., Reference Farooq, Eizad and Bae2023). Looking at several optimization studies, there are several problems with the solutions offered: first, they are robot specific, applicable only to the robot in use, and second, they represent a compromise between economy and function, while affecting the cost of the robot only to a negligible extent. In the article, they suggest further developments to solve the problem of continuous power supply for autonomous robots, such solutions are energy mining, energy cycling, and monopropellants. The goal is to provide the next generations of robots with a clean, robust, and long-lasting energy source.

The toolbox for dynamic simulation of robots has grown in recent years. In their study, Farley et al. (Reference Farley, Wang and Marshall2022) wrote a quantitative comparative study of a Husky A200 robot under simulated and real conditions, with objective comparisons. The test environment consisted of three types of terrain profiles, grass, bumps, and gravel, and the accuracy of speed and acceleration were investigated. Other sensors such as Lidar were not included in the analysis, this may be the subject of future research. Their results showed that CoppeliaSim performed best, followed slightly behind by Gazebo.

When using mobile robots, many vehicles and many tasks have to be handled at the same time, which requires a very complex simulation, as studied by López et al. (Reference López, Zalama and Gómez-García-Bermejo2022). When analyzing the control system, a detailed simulation of each AGV is not necessary. Their achievement is an event simulator built into a framework that statistically models AGV behavior using a Petri-net-based model.

Chen et al. (Reference Chen, Chen and Teng2021) present a metamodel-based simulation in their article. The simulation’s input data are taken from a real environment and the optimization of the number of AGVs for a given set of routes is performed. The utilization and throughput were also considered in the optimization. The authors’ method performs the optimization in two steps, the first step is to determine the number of AGVs at the design level. In the second step, the operational level is optimized which takes into account the charging system dispatching, positioning, and route selection rules.

Moving robots is a major issue in mobile robotics. Any related development could be interesting for the future, depending on the challenge to be met and how it can be optimally solved. Since wheel design is a typical engineering design task, Huang et al. (Reference Huang, Yin and Ong2022) in their study a design of a screw-propelled wheel using the deep generative model (DGM) method was implemented. The designed model was 3D printed and tested in comparison with a conventional screw-propelled wheel. The measured results showed an increase in effectiveness of 15%.

Lian et al. investigated scheduling strategies for industrial robots in a spatiotemporally constrained Industrial Cyber-Physical System (ICPS) framework (Lian et al., Reference Lian, Yang, Liu and Xie2022), where the robots autonomously execute a route-finding algorithm. ICPS is an evolved structure based on the 5C (Configuration, Cognition, Cyber, Conversion, Connection). The article builds on previous research that has made significant progress in the areas of task efficiency, parking time, deadlocks, congestion mitigation, routing, collision avoidance, and safety issues. The presented multilevel strategy has significantly improved scheduling, while autonomous path planning has improved the autonomy of each robot.

In her study, Szalavetz (Reference Szalavetz2022) helps to explain the fading industrial framework due to digitalization by analyzing two closely related results: first, the diffusion of general-purpose digital technologies into the resources, products, processes, value chains, and business models of traditional manufacturing industries. Second, the adaptation of traditional stakeholders to the earlier. By focusing on a specific industry, her study is intended as a springboard for research in other sectors.

In the relevant literature, we find a wide range of manufacturing system models, usually described and solved for a specific task (Kang et al., Reference Kang, Catal and Tekinerdogan2020). Artificial intelligence methods have been used in manufacturing processes for a while, including big data analytics, and more recently machine learning methods are being used in these areas (Gunasekaran et al., Reference Gunasekaran, Yusuf, Adeleye and Papadopoulos2018). In a systematic review article, Kang et al. (Reference Kang, Catal and Tekinerdogan2020) present current trends and point to possible future research areas. In the analysis’s articles, machine learning is exploited in three areas: availability, quality, and performance. Since quality and availability are measurable, they are mainly investigated, while further research is needed on the field of performance.

Li et al. (Reference Li, Zheng, Yin, Wang and Wang2023) have researched deep reinforcement learning (DRL) for facilitating personalized intelligent manufacturing. In their very comprehensive review article, they identify several application examples. Among these, they highlight the requirement for industrial robots to collaborate, including dynamic reconfiguration, ubiquitous sensing, and communication across time constraints. The DRL enables accurate and fast decisions in complex situations through representation learning. In the article, which analyzed 261 relevant publications, five main categories of algorithm-driven robotic applications were identified: manipulation, motion planning, scheduling, cloud robotics, and robot–human interaction.

The article by Dahl et al. (Reference Dahl, Larsen, Eros, Bengtsson, Fabian and Falkman2022) presents an interactive framework for new types of automation systems. The method is called dependence on formal constraints. This system is characterized by its increasing number of complex resources, such as cooperative and mobile robots. Controlling these demands, new methods instead of traditional algorithms to keep up with the increase in complexity. The built framework supports model-based control system management, such as robot positioning based on 3D geometries, and tool design. Based on the case study presented, the method was tested on a simulation. Constraint-based descriptive models require a formal model of resources, which is identified as a bottleneck by the authors of this article. The role of the automation engineer, instead of traditional programming, will be to write specifications according to the method. In this way, the manufacturing system can be managed in a more flexible way than previous methods.

Krüger et al. (Reference Krüger, Lien and Verl2009) investigated how humans can cooperate with robots to achieve flexibility and divergence. The article identifies future research in various aspects of high-level hybrid assembly, such as safety engineering, load reduction, and the coordination of the work of multiple operators and multiple machines.

Jahed and Tavakkoli-Moghaddam (Reference Jahed and Tavakkoli-Moghaddam2020) investigated a mathematical model that considers material handling systems as an intelligent transport system operated by AGVs. In their proposal, failures are also modeled, that is, several AGVs can fail simultaneously, which is unique in this field of research. They take into account the probability of machine and AGV failures and also show the effects of problems. The objective functions are production time, total delivery cost, and cost minimization due to delay penalty.

Koren et al. (Reference Koren, Gu and Guo2018) have researched reconfigurable manufacturing systems (RMS), the main goal of which is to increase the responsiveness of manufacturing systems to unpredictable changes in demand for their products. The design and operational principles of RMSs are formulated and reviewed, and the important finding of the article is that the challenges of unpredictable market demand, shorter product life cycles, greater product variety, lower production costs, and higher environmental standards are all increasing.

In their review article, Mourtzis (Reference Mourtzis2020) present an overview of the history of simulation of manufacturing systems and some future development trends). They also show that developments are moving toward a more realistic simulation, either in real time or in a digital twin. In comparison, the concept presented in this article enables fast-running simulation at a much lower level, providing valuable data for the realization of robotic manufacturing systems.

In their article, Pedrielli et al. (Reference Pedrielli, Matta, Alfieri and Zhang2018) present the Discrete Event Optimization (DEO) method for modeling simulation–optimization problems and solving of the model. These methods are characterized by their two parts: an optimization module that selects the best system configuration and a simulation module that evaluates the system performance. The simulation module acts as a black box and receives as input the result from the optimization module, and this simulation result is then received as input by the optimization module.

Chen and Cheng (Reference Chen and Cheng2021) focus on the optimization of conventional industrial robots due to the number of uncertainties and product variations in complex assembly processes. They propose a modeling methodology that builds a relationship between process parameters and system performance. Their iterative optimization algorithm is validated with two real industrial assembly flows.

Many researchers are focusing on the future of robots and their use in manufacturing systems. In their study, ElMaraghy et al. (Reference ElMaraghy, Monostori, Schuh and ElMaraghy2021). analyzes the changes on four axes: products, technology, business strategies, and production paradigms. One of their ideas is that, due to some of the problems of robots (sensor limitations from lighting conditions, real-time object detection, networking problems), the future of AI in robotics is AI applications enhanced by creative human operators. Another key idea is the use of arm-mounted effectors on mobile robots to perform certain tasks on production lines, based on sensor feedback.

Bhatta et al. (Reference Bhatta, Li and Chang2022) observed in their earlier study of flexible production systems that research is essentially focused on stationarity, while transience is only considered for fixed configurations. In today’s changing world, demands are changing very rapidly and new modeling techniques are needed. In their study, they investigate a production system served by mobile robots, in which the metric is a so-called real-time permanent product loss (PPL), which measures the performance of the production system at a given moment in time and allows the control system to act immediately. Further research is needed to develop this kind of control.

One of the crucial points in the application of mobile robots is the distance that can be achieved due to the capacity of the battery. There is a lot of research going on in this area, as increasing the battery capacity implies an increase in the robot’s mass, so there is an overall upper limit. In their article, Sperling and Kivelä (Reference Sperling and Kivelä2022) present a system in which both a battery and a supercapacitor are responsible for supplying power to the robot, called as dual-energy storage system (DESS). The robot’s control system selects the one to be used depending on the distance between the two storage locations. One result is the implementation of the concept in a mobile robot, which has been validated, and the other is the state machine model for the control method.

Hou et al. (Reference Hou, Zhang and Kim2018) also discuss the improvement of the robot’s energy efficiency in their article. With an energy management model they developed, the robot can predict its energy consumption. The model uses sensor data as well as data from the control and motion system with specified weights. This model has been tested on a four-wheeled mobile robot and the results show that the model can successfully predict the consumption during motion and even support energy management efficiently. However, it is interesting to note that the model divides the operation into three parts: standby, startup, and running, and does not take into consideration the parameter that is commonly included: the robot’s path.

In their article, Kim (Reference Kim2017) investigated the path planning and dispatch strategy of several mobile robots in a localized space for cooperative applications. One of the major challenges is to coordinate the movements of multiple robots and avoid interfering with human traffics, taking into account either the minimum distance travelled or the minimum time taken. A two-layered route planning strategy has been proposed, the first level searches for initial solutions without obstacles, and the second level tones the paths fine when dynamic obstacles are present. The method has been effectively tested on large-scale tasks with simulations.

Zhang et al. (Reference Zhang, Lin and Chen2018) summarized the methods that have been used in path planning. They also present the genetic algorithm (GA), particle swarm optimization algorithm (PSO), artificial potential field (APF), and ant colony algorithm (ACO) strategies. Finally, recommendations for future research were made. Since each method is suitable for different applications, there is no universal algorithm that can handle all the cases discussed. Research is also needed on task organization, communication, and cooperation of multirobot systems, as well as route planning at high dimension.

As we expect to use mobile robots in a variety of environments, it is also worth taking into account some practical experience with their application. Such an application is presented in the article by Szrek et al. (Reference Szrek, Jakubiak and Zimroz2022), in which a mobile robot unit is used to monitor the state of physical objects, more specifically the state of a conveyor belt. Sensor data such as RGB image, sound, gas, and so forth, are collected. In the test, a 60-m predefined path was covered with the robot and it was found that at lower speed the path was better maintained, but for most of the duration of the experiment, the deviation was no greater than ±0.02 m.

The system presented in Li et al.’s (Reference Li, Yang, Zhang and Qi2021) article analyses RMFS in high-density storage warehouses where space is limited or expensive. The idea is to combine traditional RMFS and puzzle-based storage system (RMFS). The results show that the high-density warehouse layout can save about 10% of warehouse space with the same energy consumption and robot utilization. The article also suggests that the problem could be solved by applying machine learning techniques.

Tan et al. (Reference Tan, Li and He2021) investigated an automatic vertical sorting system in their study. They described the problem using a mixed integer linear programming model, in which they considered destination stations, destinations, pick-up stations, and AGVs, and the objective function was to minimize the total sorting time. The applied particle swarm optimization algorithm solved the problem with high efficiency as demonstrated by numerical experimental results.

Tiacci’s (Reference Tiacci2020) article presents a novel event-based simulation system that uses an object-oriented approach. Modeling complex systems in an object-oriented way allows the description of system dynamics in terms of interactions between objects. The event-based graph formalism is not suitable for object-oriented and component-based simulations, where the state of the system is divided into components that implement their own behavior and interact with each other. Event graphs describe the changes in state variables as events occur. In the approach discussed in the article, the state variables are associated with objects, making the model more understandable, which is particularly useful for large complex systems.

The dynamic flexible manufacturing environment poses many challenges (unexpected pedestrian traffic, collisions, fast and slow zones, space for robots, and so on) to the movement of mobile robots, which can lead to delays even when travelling a simple route (Liaqat et al., Reference Liaqat, Hutabarat, Tiwari, Tinkler, Harra, Morgan, Taylor, Lu and Tiwari2019). In their article, Liaqat et al. developed and analyzed a new protocol that controls the movement of each robot when encountering mobile robots to ensure fast and safe passage. They set up a model, refined by a series of experiments with real mobile robots, making the model even more accurate in describing the real behavior of mobile robots.

Models are basically built using one of two approaches: either by applying some physical laws, or by self-learning based on data. While in the first case, the internal workings of the model are clear, in the second case, we are describing a behavior that is black-box like. Retzler et al. (Reference Retzler, Tóth, Schoukens, Beintema, Weigand, Noël, Kollár and Swevers2024) have combined these two methods in order to complement the errors of the physical parametric model (e.g., incomplete description of complex behaviors, noise) with data analysis-based methods. The physical interpretation of the system structure contributes significantly to improving the accuracy of black-box models.

Robots are used for many tasks in addition to the industrial transport tasks discussed in this article. Each area is not necessarily closely related to the others, but it may be worth looking at other applications, as valuable ideas can be transferred. One such area is additive manufacturing, which could play an important role in the integration of industrial robots into manufacturing systems. An interesting concept is presented in an article by Safeea et al. (Reference Safeea, Bearee and Neto2022). They have developed a collaborative robot 3D printer. The presented framework covers both hardware and software parts from the CAD model to the finished product. The implemented inverse kinematics avoids singularities due to the redundancies of the robot joints. The result is that the resulting printed parts have 25% stronger mechanical properties.

The current fourth industrial revolution is also contributing to the spread of robots, so this area should also be addressed when discussing industrial robots. One of the highly expected technologies is digital twins, from which an interesting study has also been highlighted. In their study, Culot et al. (Reference Culot, Nassimbeni, Orzes and Sartor2020) aim at a better understanding of the whole concept of Industry 4.0, reducing the confusion around the definition, which is increased by newer and newer names such as the fourth industrial revolution, smart manufacturing. In this article, previous articles are grouped according to the various keywords and from this a system of interpretation is built. They identify four types of key technologies: interfaces between the physical and digital worlds, networks, data analysis, and digital–physical process technologies.

In the future, one of the keys to control manufacturing systems could be digital twins, as researched byLiu et al. (Reference Liu, Zheng and Shang2023). They innovated the concept with a decision process based on virtual entities. They called this the digital-twin-based manufacturing system (DTMS), and decision making by these entities is a key factor affecting the accuracy of the system. The decision model must react to the state changes in real time. Inspired by biology, a mechanism that imitates instinct and learning behaviors was investigated. Finally, they propose a rule-driven decision mechanism instead of instinct-driven and conclude that learning decision mechanisms are the next potential research direction.

Balancing is a key factor for efficiency in industrial mobile robotic assembly systems, and it is therefore necessary to explore the state of the art in this field (Huo and Lee, Reference Huo and Lee2021). In their article, Jiage et al. analyzed an intelligent automation controlled production line that responds to unexpected events. Real-time information from the assembly line is used for adaptive decision making, which is controlled by a fuzzy control system, resulting in improved performance of the assembly process.

Li et al. propose a novel algorithm to maximize the productivity of AGVs (capable of carrying multiple loads simultaneously) in FMS manufacturing systems (Li and Kuhl, Reference Li and Kuhl2017). PDER (pickup-or-delivery-on-route) is an algorithm that selects a “low-cost” task (that is physically close to the robot) based on its current position. The algorithm allows robots that are not fully loaded to pick up another product and move on to their next destination. This is due to the fact that PDER prioritizes the movement of parts ready for further machining over the transport of finished parts.

The problem with using the ant colony algorithm in mobile robot path planning is that previously explored paths cannot be fully used. Hence, Hou et al. (Reference Hou, Xiong, Wang and Chen2022) have constructed and tested an improved algorithm in their article. The authors have developed and tested a faster converging version of the ant colony algorithm, enhanced with a modified roulette method. The modification consisted in making the value of the probability variable (multiplier) influenceable by another variable. They analyzed deadlock problems and developed specific strategies to avoid them, which penalize paths that reach deadlock, so that the path’s pheromone value is volatilized.

Viharos and Németh (Reference Viharos and Németh2018) used the software Plant Simulation to study a manufacturing system supported by AGVs using discrete event systems or DES. Four types of products are transported between stations and buffers by two robots. The analysis of the production system in two different layouts is supported by a graphical interface. Future directions for improvement are mentioned: extending the unit load of the robots to multiple loads; handling uncertainties such as downtime with probabilistic variables; maintenance prediction; and product order prioritization.

For mobile robots, the issue of path planning always arises, and there is a lot of research on this topic (Abdallaoui et al., Reference Abdallaoui, Aglzim, Chaibet and Kribèche2022). In their article, Abdallaoui et al. review the algorithms used for path planning, grouping them into five categories according to their type: sampling algorithms, node optimal algorithms, mathematical model-based algorithms, bio-inspired algorithms including neural networks, and finally multisession algorithms. The algorithms include traditional Dijkstra, genetic algorithm, and neural network learning. The advantages and disadvantages of each algorithm are analyzed in detail and their performance is compared, leading to the conclusion that the use of a single approach is not sufficient to achieve vehicle navigation. The best solution is achieved by a fusion method that combines two or more approaches.

Previous research by the authors of this article have already analyzed a novel approach to mobile robot modeling in manufacturing systems (Boleraczki and Gyurika, Reference Boleraczki and Gyurika2020). A solution to the mobile robot transportation problem modeled with Petri nets is presented. In addition to the start and destination positions, the robot states were characterized by the states of cargo loading, travel, and battery charging.