Research on developing digital twins based application for industrial robots nghiên cứu xây dựng bộ đôi số ứng dụng cho robot công nghiệp

Research on developing digital twins based application for industrial robots nghiên cứu xây dựng bộ đôi số ứng dụng cho robot công nghiệp Research on developing digital twins based application for industrial robots nghiên cứu xây dựng bộ đôi số ứng dụng cho robot công nghiệp Research on developing digital twins based application for industrial robots nghiên cứu xây dựng bộ đôi số ứng dụng cho robot công nghiệp Research on developing digital twins based application for industrial robots nghiên cứu xây dựng bộ đôi số ứng dụng cho robot công nghiệp Research on developing digital twins based application for industrial robots nghiên cứu xây dựng bộ đôi số ứng dụng cho robot công nghiệp

The Reasons for Choosing The Dissertation Topic

Simulating a process or a system helps humans gain a deeper understanding of the system, allowing for flexibility to adjust and change device parameters as well as to perform optimization testing during the initial planning phase Due to the advantages mentioned above, simulation has been widely researched and applied However, it has mostly been limited to static models and one-way information exchange from physical objects to digital entities The concept of the digital twin, aiming to create a digital counterpart that faithfully describes a physical device and can exchange data with it, has been gaining increasing attention from researchers Along with the strong development of digital technology and new-generation information, the ability to collect more data and process it efficiently has provided a strong foundation for the development of digital twins

The digital factory has become an inevitable trend in various industries, with the digital twin being a fundamental unit; synthesizing digital twins forms a digital factory Research on building digital twins for robots is a relatively new field, meeting practical industrial demands and promising strong development prospects in the coming years, both domestically and internationally This research is based on theoretical studies and experiments to construct a digital model that faithfully describes a robot and establishes communication connections between the physical entity and the digital model The experiments are conducted on the UR3 robot within a lightbulb assembly system The digital twin of the UR3 robot, once created, continues to be applied in tasks such as pathfinding and optimizing collaboration between humans and robots

The application of robots is becoming increasingly popular, in line with the development of the automation industry Current research in robotics continues to grow due to high market demand, a wide range of applications, and technical development potential Particularly, robot path planning has been extensively studied and applied across various generations of algorithms Optimizing path planning for robots helps reduce time and costs in robot operation processes One of the widely applied algorithms for robot path planning is the A* algorithm The A* algorithm was invented, and many improvements have been made to enhance its efficiency in the original path planning algorithm In industrial production lines, we often encounter many collaborative work scenarios between humans and robots In these collaborative systems, the advantages of robots, such as speed and precision, can be combined with human qualities like dexterity and adaptability in different situations Through an overall analysis of the digital twin and industrial robotics problem, the postgraduate has recognized that the research and development of digital twins for industrial robots is a promising research direction that can still be explored in various aspects; in particular, applying digital twins to industrial robots to enhance performance in the operations of digital factories This is the reason why the postgraduate chose the topic "Research on Developing Digital Twins-Based

Application for Industrial Robots" In this dissertation, the postgraduate focuses on

Page 9 researching methods for developing digital twins-based application for industrial robots with reference to solving problems related to robot path planning and human- robot collaboration.

Goal, Objectives, Scope, and Research Methodology

The goal of the dissertation is to gradually master the construction of industrial robots, develop software to enable the application of digital twins in optimizing robot paths and coordinating activities between humans and robots

- Developing digital twins-based application for industrial robots

- Proposing improvements to some digital twins-based applications for industrial robots with reference to solving problems related to pathfinding and human-robot collaboration

The research subjects of the dissertation are: Digital twin technology, industrial robots, methods for developing digital twins-based application for industrial robots, methods for robot pathfinding and human-robot collaboration

The scope of the dissertation research is focused on developing digital twins and their applications for the UR3 robot within the lightbulb assembly system at the Digital Factory Laboratory of the Hanoi University of Science and Technology

The research methodology involves a combination of theoretical study and practical experimentation Based on the theoretical research, including literature and previous works conducted both nationally and internationally on digital twins, industrial robotics, robot pathfinding methods, and human-robot collaboration, the study aims to understand the development of digital twins-based application for the UR3 robot Using the findings from the theoretical research, the study proceeds to implement digital twins in a real-world setting It continues to explore proposed improvements in applications related to robot pathfinding and human-robot collaboration The research involves conducting experiments, comparing theoretical and practical results, and publishing research outcomes in scientific journals and conferences, both nationally and internationally

The Scientific and Practical Significance of the Research Topic

In this research, a combination of the improved A* algorithm and digital twin technology has been used to plan the robot's path in the lightbulb assembly system The postgraduate highlights the advantages of the A* algorithm and the application of digital twin technology in mapping out the motion stages of the robot, tailored to propose an effective solution for the entire operational process Furthermore, the impact of obstacle sizes is evaluated in terms of the efficiency of one of the two methods to enhance path planning for the robot when applied to a real-world system with obstacles of varying sizes

Furthermore, digital twins are applied to optimize the collaboration between humans and robots in the lightbulb assembly production line Firstly, digital twin technology is used to find the motion trajectory of the robot The digital twin of the robot and the human is created by combining cameras to track the position and activities of the human workers in the workspace This helps prevent collisions between humans and robots in the shared workspace Subsequently, an adaptive genetic algorithm is applied to calculate the optimal movement schedule for the human workers To ensure uninterrupted operations and avoid material shortages, human workers need to observe and move to the material input conveyor and pallet input conveyor, supplying materials to the assembly system This is done to provide a continuous input of raw materials to the assembly line while allowing workers to perform their tasks in parallel with robot assembly operations The algorithm is designed to minimize the number of movements required for material retrieval, ensuring that the robot always has enough materials to follow the defined trajectory This results in labor savings and process optimization The combination of digital twin technology and the adaptive genetic algorithm optimizes the robotic movement and reduces the number of movements performed by human operators on the system.

The new findings

The new findings achieved in the dissertation are as follows:

- Development of Digital Twins-based application for the UR3 Robot in the lightbulb assembly system

- Application of digital twins in conjunction with the improved A* algorithm for robot pathfinding, comparing the cases with obstacles of constant height and varying height; consequently, proposing the use of a combination of digital twins and the improved A* algorithm suitable for each case

- Application of digital twins coupled with genetic algorithm to optimize the coordination of human and robot activities in the lightbulb assembly system The results show a reduction in the number of human movements to supply input materials to the system, ensuring that the robot can operate continuously without interruption due to a lack of materials such as lamp cap and bulb socket at the input of the assembly line

Dissertation structure

The dissertation is divided into 4 chapters with the main content summarized as follows:

Chapter 1: An Overview of Digitial Twins and Their Applications This chapter presents the history of digital twins, concepts, classification of digital twins, applications of digital twins, and the research status both nationally and internationally on digital twins

Chapter 2: Developing a Digital Twin for the Industrial Robot in the Lightbulb Assembly System This chapter presents the practical implementation experiment of the lightbulb assembly system using the UR3 robot The main contents include building the operational procedure of the lightbulb assembly system, analyzing the direct and inverse kinematics of the UR3 robot, thereby developing a digital model that accurately describes the geometric characteristics and motion of the UR3 robot Finally, it establishes a communication link between the virtual and real UR3 robots

Chapter 3: Application of Digital Twins in Pathfinding for Robots This chapter analyzes the problem of pathfinding for robots It conducts research, measurements, and comparisons of the robot's travel time when applying the A* algorithm with the digital twins method in various cases with different obstacle characteristics, including constant and varying heights, as well as different values of velocity and acceleration Consequently, it presents the effectiveness of robotic pathfinding using the A* algorithm and the digital twins method under specific conditions related to obstacle characteristics

Chapter 4: Application of Digital Twins in Human-Robot Collaboration This chapter explores the problem of human-robot collaboration, the combination of genetic algorithms and digital twins to optimize human operations within the lightbulb assembly system

OVERVIEW OF DIGITIAL TWINS AND THEIR

Introduction

The technology of Digital Twins has been in existence since the 2000s In recent years, the rapid development of information technology (such as big data, cloud computing, artificial intelligence, etc.) has created favorable conditions for the robust growth of Digital Twin technology, attracting significant attention from researchers with a substantial increase in the number of research papers Digital Twins are not only used in a single phase but also have the ability to be used throughout the lifecycle of a system: from (i) planning, designing, optimizing parameters, testing, (ii) creating the actual system, (iii) operation, fault prediction, maintenance planning, lifespan prediction, to (iv) ceasing operation, eliminating from the operational system Digital Twins have wide-ranging applications across various industries (information technology, transportation, aviation, mechanical engineering, construction, healthcare, etc.), helping optimize system operations and reduce costs Alongside this, there is an increasingly widespread application of robotics in industrial production systems The problem of robot pathfinding and the coordination between humans and robots are topics of significant interest with numerous practical applications

In this section, the postgraduate will present the development of digital twins, their applications in various stages of the manufacturing process, and in different industries and fields Additionally, the postgraduate will provide an overview of the research landscape, both domestically and internationally, regarding digital twins and their applications in industrial robotics.

The History of Digital Twin Development and Milestones

The NASA Apollo space program was the first to introduce the concept of "Twin" The program constructed two identical spacecraft so that the spacecraft on Earth could reflect, simulate, and predict the conditions of the other spacecraft in space The remaining spacecraft on Earth served as a twin to the spacecraft carrying out the mission in space [1] The term "Digital Twin" first appeared in the research of L.A Hernández and S Hernández [2] Digital twins were initially used to perform repetitive adjustments in the design of a road network However, this term was later widely recognized under the name "Digital equivalent to a physical product" introduced by Michael Grieves at the University of Michigan in 2003 [3]

The concept of "Product Avatar" was introduced by Hribernik and colleagues in their research in 2006 [4], which is a concept similar to the Digital Twin The concept of Product Avatar aimed to build an information management architecture to support

Page 13 bidirectional information flow with a product-centric perspective Research on the concept of "Product Avatar" can be found in studies prior to 2015 [5-7] However, the concept of Product Avatar has been largely replaced by "Digital Twin" since after

The detailed initial definition of the Digital Twin was provided by NASA in [8] Since then, Digital Twin technology has become a timely research topic in the aerospace industry In 2014, Michael Grieves published a document to provide a more detailed explanation of this concept The conceptual model of Digital Twins, implementation requirements, and use cases have been extensively discussed in [3]

In 2017, the Gartner company listed "Digital Twin" as one of the top 10 strategic technology trends, ranking it 5th They predicted that there would be numerous applications of Digital Twins within 3-5 years [9] ] In the following two years, Gartner continued to include "Digital Twin" in the top 10 strategic technology trends, ranking it 4th [10, 11]

The concept of Digital Twins was initially more descriptive and lacked supporting technologies at that time However, the development of advanced technologies has paved the way for the rise of Digital Twins Table 1 lists research on ScienceDirect and Scopus over a decade from 2011 to 2020 related to Digital Twins [12] showing that since 2016, the number of research studies has increased exponentially Digital Twins have become a frequently searched term and have attracted significant attention in various industries and academia

1.2.2 Key Milestones in the Development of Digital Twin Technology

Figure 1.1 summarizes the important milestones in the development process of Digital Twins according to the report [13, 14]

Figure 1 1 Key Milestones in the development of digital twin technology

Digital twin concept and classification

Table 1.1 provides a summary of some definitions of Digital Twins and research over time to illustrate the development of the concept during the period from 2019 and earlier [15]

It can be observed that the general trend, in the early years of this period, most articles defined Digital Twins as highly realistic simulation models that could be used in various industries, without considering real-time connections to physical objects

In more in-depth research works, many scientists began to focus on the bidirectional mapping between physical objects and virtual objects However, most of these studies did not distinguish Digital Twins from general computational and simulation models Below are some notable research works on Digital Twins

Zheng and colleagues [16] discussed the concept and characteristics of Digital Twins from narrow to broad meanings They proposed an application framework consisting of three parts: the physical space, the virtual space, and the information processing layer During application, a Digital Twin can establish a full mapping between the real system and the virtual system, with the virtual model operating throughout its lifecycle and optimizing real-time operation for the entire process Schluse and Rossmann [17] introduced a new concept of "Experimentable Digital Twins" and described how this type of Digital Twin can perform development processes based on simulations to simplify operational processes, allowing detailed system-level simulations and the deployment of intelligent systems Subsequent research [18] related to Experimentable Digital Twins (EDT)

Bao and colleagues [19] provided definitions for three types of Digital Twin models from the perspective of the production process to the final assembly stage: Product Digital Twin, Process Digital Twin, and Operation Digital Twin

Ullah [20] proposed the classification of three types of Digital Twin: object twin, process twin, and phenomenon twin

Despite some variations in explanations, there is a consensus on the characteristics of Digital Twins, making them applicable in various industrial fields The fundamental idea of a Digital Twin is quite simple: accurately link a physical object with a digital counterpart in real-time However, it can be challenging to provide a specific definition

Many Digital Twin models or reference models have been proposed Stark and colleagues [21] developed an "8D Digital Twin Model" to delineate and classify Digital Twins In this model, four dimensions represent the behavioral capabilities of the Digital Twin, while the remaining four dimensions reflect the environment and context of the Digital Twin

Table 1 1 Definitions of digital twins in studies from 2019 and earlier

No Ref Time Definition of digital twins Main points

A Digital Twin is a probabilistic, multi-scale, multi-physics integrated simulation of a vehicle or system that uses the best available physics models, updates sensor values, stores operational history, etc., to reflect the entire lifecycle of its physical counterpart

A Digital Twin functions as a lifecycle and verification management model derived from a prototype It encompasses models and simulations incorporating the initial state of a vehicle, payload, environmental factors, and specific vehicle histories This approach facilitates high-fidelity modeling of individual aerospace vehicles across their entire operational lifecycle

3 [23] 2015 "Digital Twins" commonly refer to highly realistic models representing current processes and their behaviors as they interact with the real-world environment

Digital twins are virtual substitutes for objects in the real world, including virtual representations and communication capabilities that create intelligent entities that operate as smart nodes within the Internet of Things and the Internet of Services

A 'technical digital twin' refers to a digital copy of a factory, machinery, actual workers, etc It is created to expand independently, update automatically, and be globally accessible in real-time

Improved optimization algorithms, enhanced computing capabilities, and the accessibility of extensive datasets now facilitate the utilization of simulations for real- time control and optimization of products and manufacturing systems This concept is commonly known as the Digital Twin

Real-time control and optimization

A digital twin is a collection of virtual information structures that fully describe a potential or actual physical product, produced from the micro-level element to the macro-level geometric level

A digital twin is an abbreviation for a specific technical model in which individual physical objects are linked to a digital model that reflects the real-time status and behavior of those objects

9 [28] 2/2018 A digital twin is a precise virtual replication of a "technical entity," such as a machine, component, or environmental element, maintained in a one-to-one correspondence Virtual replica

10 [29] 5/2018 A digital twin model is an accurate, real-time network replica of an existing physical production system that encompasses and represents all of its functionalities Virtual replica

A digital twin is a multi-domain, highly accurate digital model that integrates various fields such as mechanical, electrical, hydraulic, and control, achieving an exceptionally high level of fidelity

12 [31] 8/2018 A digital twin represents a dynamic digital replica of physical devices, processes, and systems, capable of comprehensive monitoring throughout their lifecycle A vivid replica

13 [32] 9/2018 The rich digital representation of objects/entities and processes in the real world, including data transmitted by sensors, is referred to as the digital twin model

A digital twin is fundamentally a unique, living model of a physical system, enhanced by technologies that enable multi-physics simulation, machine learning, AR/VR, cloud services, etc

15 [34-36] 12/2018 Building Information Model (BIM) is a digital twin

16 [37] 12/2018 A digital twin flexibly embodies physical entities along with their functions, behaviors, and operational rules

The new technology that provides access to real-time models of the current state of processes and their behaviors as they interact with their environment in the physical world is referred to as “digital twin”

A digital twin is a virtual counterpart of a physical system (twin system) that is continuously updated with data about the performance, maintenance, and health status of this system throughout its physical system's lifecycle

19 [40] 2/2019 A digital twin is a virtual object or a collection of virtual objects defined within a digital virtual space, having a mapping relationship with real-world objects in physical space Mapping

A digital twin is described as a digital copy of a physical device It gathers real-time data from the actual device and derives information that might not be directly measured on the hardware itself

A digital twin can be viewed as a model where selected online-measured parameters are dynamically synchronized between the simulation world and the real world in an adaptive and bidirectional manner

Schleich and colleagues [43] delved into exploring the capabilities of the digital twin reference model, including aspects like interactivity, scalability, upgradability, and fidelity Their study also encompassed diverse activities conducted using this reference model throughout the product lifecycle, involving processes such as conversion, assessment, integration, and disassembly of system components

Digital twin application

- Digital twins can be applied in every phase throughout the product lifecycle

In this phase of the digital twin, a virtual model is created, and multiple team members can participate, providing input based on their personal experiences and desired product features With the virtual model, iterative editing is performed to achieve a high level of completeness Versions are easily saved for comparison Parameters can be adjusted to optimize the design This helps minimize costs and implementation time when transitioning to the real-world deployment

The industrial manufacturing process involves the transformation of raw materials at the input into finished products at the output With the rapid development of technology and its application in the production line, manufacturing has shifted from conventional processes to intelligent processes Digital twin technology facilitates the interaction between the digital model and the physical model During the manufacturing phase, digital twins can help monitor real-time systems, control manufacturing, predict performance, optimize collaboration and interaction between humans and robots, assess and optimize processes, manage assets, and plan manufacturing

In this phase, the product has been delivered to the end-users and is beyond the control of the manufacturer and supplier Users are primarily concerned with the reliability and utility of the product, while manufacturers focus on the real-time operational status of the product, warranty strategies, product maintenance, etc The "digital twin" is a highly realistic real-time representation of physical entities integrated with multidisciplinary models (geometry, mechanics, materials, electrical, etc.) It can help predict maintenance, detect and diagnose faults, monitor states, and predict the performance of the actual product Additionally, the virtual testing applications of digital twins assist in verifying specific operations that, if they fail, could result in significant damage if performed on the actual product

In reality, the retirement phase is often overlooked, and there is very little research on this phase Information about the system or product's operations is usually lost when the system ceases to function The next generation of the system or product often encounters similar issues that could have been avoided by utilizing the knowledge of those who worked on it before In the retirement phase, the digital twin contains the entire life cycle history of the physical entity and can preserve and use information at a low cost in the digital space

- Digital twins can be applied in various industries and fields

Manufacturing is the most common research area for digital twins and represents a significant portion of digital twin research Most studies focus on optimizing production planning, simulating manufacturing, monitoring and predicting product performance, and aiming for sustainable production Another popular field is smart buildings and cities, which concentrate on monitoring the sustainability of structures, building management and control, optimizing project planning, and predicting maintenance Information and Communication Technology (ICT) is also a prominent focus in digital twin research and has wide applications in edge computing systems, communication security, and cloud service monitoring Next, energy-related digital twin research focuses on power systems,

Page 22 fault diagnosis, and optimizing power plant operations Research topics related to automotive engineering, aerospace, healthcare, and medical care have a similar proportion, mainly focusing on product monitoring, prediction, testing, and simulation Finally, educational applications of digital twins have been on the rise in recent years due to the trend of online teaching and learning Various research fields are grouped together, including mining, agriculture, chemistry, etc [48]

Among these applications, there are two applications that have attracted significant attention from researchers and have many practical applications in production operations: the use of digital twins in robot path planning and in human-robot collaboration They are further elaborated in Sections 1.4.2 and 1.4.3 below

1.4.2 Digital twin application for robotic path planning

Planning the path for industrial robots is a crucial element in improving the overall performance of an automation system Robotic path planning involves various algorithms, often created before the robot operates, to determine its movement

In essence, path planning algorithms dictate how an industrial robot's arm should approach the next part of the process, how it interacts with that part, and how it must orient itself to achieve optimal productivity while avoiding collisions Path planning for industrial robots is an essential component of automated manufacturing systems, ensuring that path planning is accurate, safe, and efficient

- Offline programming for robot path planning

In many instances, the robot's path planning is conducted offline, prior to its execution and before tackling new tasks This process commonly occurs within an offline programming environment, utilizing lifelike simulations of the robot's operational conditions This approach enables programmers to anticipate and compute automation variables within the working environment, facilitating precise and calculated planning of the robot's path

Offline programming has emerged as a vital tool for robot integrators and is eagerly anticipated by robot users due to its substantial reduction in the time needed to instruct the robot regarding specific paths Presently, a majority of robot paths are planned using this method due to its efficiency

- The role of appropriate robot path planning in production

When robot path planning is done correctly, industrial robots can efficiently perform the following tasks Robot path planning plays a significant role in the following aspects:

- Robot Accuracy: The robot's path needs to be meticulously planned to handle tasks effectively with minimal or no errors

- Task Repetition Capability: Once a robot's path is precisely established, it can repeat the same task thousands of times without any alterations, thereby enhancing throughput

- Product Quality: Products crafted with high accuracy and repeatability experience fewer errors, leading to an overall increase in quality and the production of higher- quality items

Robot path planning is extremely important to enable robots to carry out assigned tasks effectively, and in this way, it plays a crucial role in the manufacturing process [49]

1.4.3 Digital twin application for human-robot collaboration

Collaboration between humans and robots in manufacturing systems aims to create a shared workspace where humans and robots can work alongside each other Human-robot collaboration in manufacturing involves assessing that robots must adapt to human behaviors by dynamically changing their tasks

The concept of human-robot collaboration was first implemented with industrial support robots (such as the KUKA LWR 4) in 2008 [49] According to Hentout et al [50], human- robot collaboration can be classified into the following levels: (i) coexistence between humans and robots, (ii) coordination between humans and robots, and (iii) cooperation between humans and robots, where cooperation between humans and robots can be further categorized into physical collaborations and contact-less collaborations Another classification by Haddadin et al [51] is based on the physical proximity between humans and robots This classification categorizes human-robot collaboration as more intimate than human-robot cooperation Therefore, human-robot cooperation (HRCoop) involves closer interactions compared to human-robot collaboration (HRC) In these three classifications, human-robot cooperation (HRCoop) represents the closest proximity, while coexistence between humans and robots (HRCox) is at the farthest distance On the other hand, Kolbeinsson et al [52] mentioned that HRC is based on how humans and robots share workspace and tasks HRC represents the highest level of cooperation between humans and robots, where robots can operate without encountering any barriers.

The research status both domestically and internationally

The digital twin (DT) concept is becoming a new trend in solving practical problems in various industries, with its most prevalent application being in manufacturing systems Digital twins offer the possibility of applying them throughout the entire lifecycle of a system, across multiple stages and processes, to increase efficiency and performance An essential component of modern manufacturing systems is industrial robots, and many research efforts have been directed towards digital twins, particularly digital twins for industrial robots, route planning problems, and human-robot collaboration Some notable research findings in these areas will be presented in the following sections

- The research by Ali Ahmad Malik and Arne Bilberg from the University of South Denmark, published in 2018, focused on "Digital twins of human-robot collaboration in a production setting" [53] In this work, they presented a digital twin framework that supports the design, construction, and control of collaboration between humans and machines Computer simulations were used to develop a digital replica of the collaborative working environment between humans and robots for assembly tasks This digital replica remains continuously updated throughout the lifecycle of the production system by reflecting the physical system, allowing for continuous, rapid, and safe improvements The key contributions of this research were as follows: (1) It demonstrated the need and utility of digital twins for designing, developing, and operating human-robot production systems; (2)

It proposed a framework for implementing digital twins for an HRC (Human-Robot Collaboration) workstation; (3) It presented a case study to illustrate the practical application of the proposed framework in an assembly workstation and its advantages With each change in production parameters, behaviors could be simulated and results evaluated without any financial risk or physical harm to humans in the actual production environment Digital twins enable conducting hypothetical tests and estimating outcomes, even without real-time connections to the physical system With advancements in information and communication technology, digital twins can continuously evolve in real-time, providing higher utility at the system level

- The research conducted by Heikki Laak, Yoan Miche, and Kari Tammi at Aalto University and Nokia Bell Labs in Finland, published in 2019, centered on "Prototyping a Digital Twin for Real-Time Remote Control Over Mobile Networks: Application of Remote Surgery" [54] In this study, the authors implemented a digital twin for the UR3 robot to support remote surgery The system consisted of a robot arm and a virtual reality (VR) system connected via a 4G mobile network Over 70 test users were used to evaluate the system The remote operation of a human hand was successfully achieved with feasible accuracy based on the test results

- C J Liang et al from the University of Michigan, USA, published the paper "Bi- Directional Communication Bridge for State Synchronization between Digital Twin Simulations and Physical Construction Robots" in 2020 [55] This paper outlines the initial establishment of an online robot digital twin system designed for human-robot collaboration within digital construction and manufacturing realms This system incorporates virtual and physical robot modules alongside communication modules ROS Gazebo and rviz software were employed for crafting the virtual robot modules Connection between the digital twin and physical robot module occurs via the MQTT Bridge within the communication setup, facilitating the exchange and synchronization of robot arm joint angles MATLAB and MoveIt! were utilized by the research team to strategize and control the robot arm within the virtual module, subsequently transmitting commands for execution to the physical robot module Additionally, they devised a Pose Checking Algorithm (PCA) aimed at guaranteeing synchronization between the poses assumed by the two robots This system was put into practice using a KUKA KR120 robot arm within a digital manufacturing laboratory The researchers evaluated the system by comparing joint angles between the virtual robot and the physical robot in a trajectory plan, calculating average

Page 25 and maximum errors The results showed that the proposed DT system for online robots could plan robot trajectories inside a virtual environment and execute them in a physical environment with high accuracy

- The research team led by Tang XiangRong, Zhu Yukun, and Jiang XinXin at YanBian University in China published a paper titled "Improved A-star algorithm for robot path planning in a static environment" in 2021 [56] The A-star algorithm is a simple path planning algorithm that does not require solving complex analytical problems and is highly applicable However, compared to other path planning algorithms, it consumes a large amount of memory space This research addresses this issue and introduces three new concepts: "bidirectional search," "guidance path," and "list of key points," which improve the directionality of the search for a path from the starting point to the destination The A- star algorithm is optimized using these concepts and is applied to indoor environments Through MATLAB simulation experiments, the research demonstrates that the optimized algorithm is feasible and can reduce memory usage by more than 60% compared to the traditional A-star algorithm

- The research team led by Stepan Bratchikov, Artur Abdullin, Galina L Demidova, and Dmitry V Lukichev at ITMO University in Russia published a paper titled "Development of Digital Twin for Robotic Arm" in 2021 [57] This research focused on developing a digital twin for a robotic arm using dynamic modeling of the robot Based on the given geometric control characteristics, they obtained the input coordinates of the end effector's maximum point and the relationship between the orientations of the joint connections (links) angles in space with each other These angles were used as reference signals for the corresponding motor control loops at the robot's arm joints The dynamic responses were analyzed using the Matlab/Simulink/SimMechanics environment The CAD model of the robotic arm was automatically generated from the mathematical model mentioned earlier while preserving the information about the connections between components The research aimed to develop an accurate device model in data space In this paper, a control design method based on the kinematics of the connections was proposed, and the trajectory of the operational motion was described and analyzed using Quaternionic motion analysis methods

- Gaurav Garg et al from the University of Tartu, Tallinn University of Technology in Estonia, and Tallinn University of Technology in Turkey published a paper titled "Digital Twin for FANUC Robots: Industrial Robot Programming and Simulation Using Virtual Reality" in 2021 [58] This paper introduces a digital twin model tailored for supporting the online/remote programming of FANUC robot cells by creating a 3D digital replica of the real-world setup This model consists of two primary components: (1) the physical model, representing the FANUC robot, and (2) the digital model, utilizing Unity (a game development platform) alongside specialized plugins catering to virtual and augmented reality devices One of the key challenges in the current robot programming approach is the creation and alteration of code for robot trajectories within the digital twin structure Through the utilization of a digital twin setup coupled with virtual reality, the research team observed the replication of trajectories between the digital and physical robots Simulation analysis revealed a latency of approximately 40 milliseconds, with error ranges from -0.28° to 0.28° observed on the robot's joint motions within the simulation environment and -0.3°

Page 26 to 0.3° on the real robot's joint motions Absolutely, with such minimal latency and a high level of accuracy, this model stands as an effective solution for various industrial applications

- The collective of researchers involving Milan Groshev, Carlos Guimaraes, Jorge Martín-Perez, and Antonio de la Oliva from Universidad Carlos III de Madrid in Spain published a paper titled "Towards Intelligent Cyber-Physical Systems: Digital Twin meets Artificial Intelligence" in 2021 [59] In this paper, they discuss the role of artificial intelligence (AI) in Industry 4.0, primarily related to Digital Twins AI, with the assistance of machine learning (ML) algorithms, opens up many opportunities to optimize reliability, robustness, and performance in the digital twin context The paper introduces the concept of DT models, cloud computing, and integration with emerging networking technologies such as 5G and WiFi 6E, along with edge and fog computing and physical processes The research team then identifies and analyzes sample AI applications for DT, from application- level to infrastructure-level Experimental validation was conducted to demonstrate the applicability of AI for predicting the next motion using data from a digital twin of a robotic arm

- The study titled "An integrated mixed reality system for safety-aware human-robot collaboration using deep learning and digital twin generation" was published in 2022 and authored by Sung Ho Choi, Kyeong-Beom Park, Dong Hyeon Roh, Jae Yeol Lee, Mustafa Mohammed, Yalda Ghasemi, and Heejin Jeong These researchers are affiliated with Chonnam National University in South Korea and the University of Illinois at Chicago in the United States [60] In this research, they proposed an integrated mixed reality (MR) system for safety-aware Human-Robot Collaboration (HRC) using deep learning and digital twins Their approach accurately measures the minimum safe distance in real-time and provides MR-based task support for operators The prosposed method combines Mixed Reality (MR) with safety-oriented monitoring, utilizing smart MR glasses to provide user- centric visuals for safe and effective Human-Robot Collaboration (HRC) It employs two RGB-D sensors—one capturing 3D point cloud data of the physical environment and the other tracking the operator's 3D skeleton information These sensors reconstruct and monitor different areas within the workspace A rapid global registration method partially merges the two environmental scans, while a deep learning-based segmentation technique enhances registration between the physical and virtual robots (digital twin) In contrast to prior research utilizing 3D point cloud data, this study introduces a straightforward yet efficient 3D compensation method for determining safe distances This method, based on the robot's digital twin and the human skeleton, enables real-time application without compromising the accuracy of safe distance calculations for Human-Robot Interaction (HRI)

- The research team led by Chengxi Li, Pai Zheng, Shufei Li, Yatming Pang, and Carman K.M Lee from The Hong Kong Polytechnic University and the Laboratory for Artificial Intelligence in Design in Hong Kong, China, published a study titled "AR-assisted digital twin-enabled robot collaborative manufacturing system with human-in-the-loop" in 2022

[61] Meanwhile, AR (Augmented Reality) is a technology that allows the creation of virtual objects generated by computers to interact with the physical environment It is an important component of the concept of Industry 4.0, enabling operators to access both

Page 27 physical and virtual information in a combined scenario and interact with virtual objects

AR is suitable for remote control of robots, and it can be used in various applications to bridge the gap between humans and machinery systems For example, it can be used for production guidance and facilitating collaboration between humans and robots This research has proposed a mechanism for remote operation and coordination of multiple robots in assembly tasks The physical robots' Digital Twins are used to develop two remote control modes: real-time Cyber2Physical and planned Cyber2Physical modes Physical2Cyber mode and embedded display modules are also used to provide operators with real-time insights into the production environment Reinforcement Learning (RL) algorithms are used to control the motion and planning of multiple robots The research also provides a bridging approach to train the learning algorithms in a virtual environment and deploy them in a physical environment

- Xiaowei Guo from the University of Southern California in the USA published a paper titled "A Modified Q-Learning Algorithm for Robot Path Planning in a Digital Twin Assembly System" in 2022 [62] This research focused on developing a digital twin system for assembly processes, including real and virtual interaction feedback, data analysis, and iterative optimization modules for decision-making In the virtual environment, the study proposed a Q-learning algorithm to address the problem of path planning during product assembly The proposed algorithm accelerated convergence by introducing dynamic rewards, optimizing the initial Q-table through knowledge and experience transfer using Case-Based Reasoning (CBR), and preventing intrusion into confined areas through obstacle avoidance methods Experiments were conducted using a six-degree-of-freedom UR10 robot to verify the algorithm's performance in three-dimensional pathfinding The test results demonstrated that the modified Q-learning algorithm significantly improved pathfinding performance compared to the original Q-learning algorithm

Conclusion of Chapter 1

The technology of digital twins presents a new and promising direction for applications in industrial robotics, enhancing precision and performance This chapter has provided an overview of digital twins, industrial robotics, path planning applications for robots, human- robot collaboration, and the current research status both nationally and internationally It is noted that apart from the aforementioned applications of digital twins in the transportation sector, there have been no domestic studies on the application of digital twin technology in industrial robotics In the world, there is also currently no report on the combination of digital twins with the improved A* algorithm in pathfinding for robots as well as the application of genetic algorithm in optimizing the ergonomics of human-robot collaboration

Based on this context, the postgraduate has identified the topic "Research on Developing Digital Twins-based Application for Industrial Robots" and aims to accomplish the following tasks:

- Develop a digital twin for the UR3 robot in a lightbulb assembly line

- Apply the digital twin in conjunction with the A* algorithm for robot path planning

- Apply the digital twin in conjunction with the genetic algorithm for human-robot collaboration

These topics will be further analyzed and explored in the subsequent chapters of the dissertation

DEVELOPING A DIGITAL TWIN FOR THE INDUSTRIAL

Lightbulb assembly system

The image of the actual lightbulb assembly system is described in Figure 2.1

The operational cycle of the system is described through an algorithm flowchart, as presented in Figure 2.2 Following that, the algorithm flowchart for supplying sockets onto pallets, supplying caps on the material conveyor, pressing and attaching caps to the sockets, and completing the product is outlined in Figure 2.3 Lastly, the algorithm flowchart for product retrieval is depicted in Figure 2.4

 Cycle of supplying lightbulb caps, sockets and completing lightbulb assembly

Remove defective product Re-start

Figure 2 3 Algorithm flowchart for supplying lightbulb caps, sockets and completing lightbulb assembly

Figure 2 4 Algorithm flowchart for product return cycle

Remove defective product Re-start

Kinematic calculations and development of digital twin for the UR3 robot 32 1 Kinematic calculations of the UR3 robot

2.2.1 Kinematic calculations of the UR3 robot

Robot model and Denavit-Hartenberg (DH) coordinate systems

The robot in question is a six-degree-of-freedom robot, wherein the first three joints are of a revolute type (similar to the functionality of a human arm) responsible for positioning, and the last three joints are equivalent to spherical joints, serving as orientation joints for the robot's end-effector With six degrees of freedom, the robot ensures sufficient flexibility and complexity in both positioning and orientation tasks While there is a wide variety of robot types and quantities, the majority of industrial robots have this six-degree-of-freedom structure It can be considered a typical and common type of robot in the industrial robotics field

Figure 2 5 UR3, UR5 and UR10 industrial robot product line

Figure 2 6 Kinematic parameters of the UR3

On Figure 2.5, there is an image of various UR robot types These robots come in different sizes but generally have a similar shape Starting from real images, we can construct the motion model of UR robots as shown in Figure 2.6 [63] In this model, we assign dimensions on the figure with parameters as follows: 𝑂 0 𝑂 1 = 𝑑 1 , 𝑂 1 𝐴 = 𝑑 2 , 𝐴𝑂 2 𝑎 2 , 𝑂 2 𝐵= 𝑑 3 , 𝐵𝐶 = 𝑎 3 , 𝐶𝑂 3 = 𝑑 4 , 𝑂 4 𝑂 5 = 𝑑 5 , 𝑂 5 𝑂 6 = 𝑑 6 Using the Denavit-

Hartenberg (DH) matrix method [5,19,20], we establish coordinate systems for robots in the shape shown in Figure 2.7 After establishing these coordinate systems, we determine the table of DH dynamic parameters as provided in Table 2.1

Figure 2 7 Motion model of the UR robot

Table 2 1 D-H parameter table of the UR3 robot on the lightbulb assembly table [63]

𝑎 𝑖 : The distance between two consecutive joints along 𝑋 𝑖

𝑑 𝑖 : The distance between two consecutive joints along 𝑍 𝑖−1

𝛼 𝑖 : The angle of rotation around 𝑋 𝑖 between 𝑍 𝑖−1 and 𝑍 𝑖

𝜃 𝑖 : The angle of rotation around 𝑍 𝑖−1 between 𝑋 𝑖−1 and 𝑋 𝑖

From the way we construct the coordinate systems above, to transform from the (i-1)-th coordinate system to the i-th coordinate system, we need to perform four steps as follows

[19,20]: First, rotate around the 𝑧 𝑖−1 axis by an angle

𝜃 𝑖 ; Next, translate along the 𝑧 𝑖−1 axis by a distance di, then translate along the 𝑥 𝑖 axis by a distance 𝑎 𝑖 and finally, rotate around the 𝑥 𝑖 axis by an angle 𝛼 𝑖 In this case, the transformation matrix from the (i-1)-th coordinate system to the i-th coordinate system is the product of these four basic homogeneous transformation matrices Therefore, we have:

1 cos cos in in in os sin os os in os in

From the DH dynamic parameters table (Table 2.1), by substituting the corresponding parameters into Equation (2.1), we can quickly calculate the transformation matrices for each step as follows:

From the transformation matrices above, we can determine the homogeneous transformation matrix given by the formula [5,19,20]:

Note: In the matrices above, we introduce the following symbols:

Page 36 cos( ); cos( ); ( ) sin( ); sin( ); ( ) i i ij i j ijk i j k i i ij i j ijk i j k c q c q q c q q q s q s q q s q q q

Determination of the angular velocity and angular acceleration of the joints of the UR3 robot

To find the angular velocities of the joints of the UR3 robot, we can use the following formula [5,19]:

Where R i is the cosine direction matrix of joint i relative to the fixed coordinate system, and these matrices are determined based on the transformation matrices 𝐴 𝑖 The matrix

From Equation (2.11), we can determine the matrices R i , which have the following form:

After obtaining the cosine direction matrices and applying Equation (2.10) while considering Equation (2.11), we can determine the angular velocity vectors of the joints of the UR3 robot

 The angular velocity vectors of the joints of the UR3 robot when projected onto the coordinate systems of the joints are as follows:

 The angular velocity vectors of the joints of the UR3 robot when projected onto the fixed coordinate system are as follows:

Similarly, by taking the time derivative of Equation (2.10), we obtain the Jacobian matrix of the angular acceleration vector of the joints in the following form:

From Equations (2.13) and (2.14), it is straightforward to deduce the angular acceleration vectors of the joints of the robot

Velocity and acceleration at the specified position of the operational phase of UR3 robot

From Equation (2.12), it can be inferred that the position of the end-effector point is the first three components of the fourth column of the matrix 𝐴 6 Therefore, we have

Taking the time derivative of Equation (2.14), we obtain the velocity of the end-effector point:

Continuing to differentiate the velocity projections, we obtain the projections of the acceleration vector at the end-effector point on the fixed axes

Establishing the kinematic equations of the robot

The system of robot dynamics equations provides the relationship between the position of the end-effector and the orientation of the manipulator, along with the coordinates of the joints This system of equations plays a crucial role in the analysis of inverse kinematics problems later on In this section, we will establish these equations

From what we have discussed earlier, we know that the homogeneous transformation matrix representing the relationship between the coordinate system attached to the end- effector and the fixed coordinate system has the form:

On the other hand, the homogeneous matrix describing the operational phase has the form:

Where the vectors n n n n ( x , y , z ); ( s s s s x , y , z ); ( a a a a x , y , z ) are unit vectors along the three coordinate axes of the coordinate system attached to the end-effector These three vectors represent the orientation of the end-effector, but the vector r P ( x P , y P , z P ) represents the position of the end-effector (essentially the origin of the coordinate system attached to the end-effector) in the fixed coordinate system From this, the dynamic equations system can be formulated as:

Expanding Equation (2.17) explicitly, we obtain the dynamic equations system for the UR3 robot as follows:

Note that in Equation (2.18), the expressions on the left-hand side represent the components related to the end-effector, while the expressions on the right-hand side contain the dimensions of the joints and joint angles Equation (2.16) consists of 12 equations, including 3 equations related to position and 9 equations related to orientation However, only 3 out of the 9 orientation equations are independent Typically, the following 6 equations are chosen as the system of dynamic equations for the robot:

Inverse kinematic analysis of the UR3 robot

For the inverse kinematics problem, starting from the dynamic equations system with components related to both orientation and position in the matrix T in Equation (2.16), along with the known dynamic dimensions of the robot, we need to find the joint motions

For the inverse kinematics problem of robots, there are typically two main approaches: numerical methods and analytical methods Numerical methods can solve general problems for most robot configurations but often require extensive computational time due to the use of iterative algorithms Without reducing the computation time, they may not be suitable for real-time control applications On the other hand, analytical methods, while having specific methods corresponding to different robot configurations, may not be universally applicable to all robots In many cases, solving robot dynamics analytically can be challenging However, a significant advantage of analytical methods is that the solutions are in the form of analytical expressions, allowing for fast computations, which is suitable for real-time control tasks In the context of calculating robot inverse dynamics, our group has chosen to use the analytical method

Equation (2.17) can be re-written as follows:

Multiplying both sides of Equation (2.22) by D 𝑖 −1 , we have:

Replacing D 6 = T into Equation (2.23), we have:

For i = 1 to 5, we obtain five matrix equations Then, by equating the corresponding elements of these matrix equations, we will select six independent equations to determine the joint variables q i However, as mentioned earlier, the analytical method is not universally applicable to all types of robots Essentially, selecting these independent equations depends on the specific configuration of each robot, and for each specific configuration, suitable equations have been identified For the robot under consideration here, which has two, three, and four joint axes parallel to each other, the following method will be used [64]

Starting from Equation (2.24), we have:

From the matrices F1=0, F2=0, F3=0, we can derive the following 6 equations needed to solve the inverse dynamics problem for the UR robot with the given configuration:

Note : If we use the three Roll-Pitch-Yaw angles φ, θ, and ψ to determine the orientation of the end-effector, then we have:

A = [ cos 𝜃 cos 𝜃 cos 𝜑 sin 𝜃 sin − sin 𝜑 cos cos 𝜑 sin 𝜃 cos + sin 𝜑 sin sin 𝜃 cos 𝜃 sin 𝜑 sin 𝜃 sin + cos 𝜑 cos sin 𝜑 sin 𝜃 cos − cos 𝜑 sin

− sin 𝜃 cos 𝜃 sin cos 𝜃 cos ]

Hence, it can be deduced

𝑠 𝑥 = cos 𝜑 sin 𝜃 sin − sin 𝜑 cos

𝑠 𝑦 = sin 𝜑 sin 𝜃 sin + cos 𝜑 cos

𝑎 𝑥 = cos 𝜑 sin 𝜃 cos + sin 𝜑 sin

𝑎 𝑦 = sin 𝜑 sin 𝜃 cos − cos 𝜑 sin

Next, we will solve the system of 6 equations above to find the joint variables q 1, q 2, q 2, q 4, q 5 và q 6

From Equation (2.29), we can infer:

Note : atan2(y,x) function can be defined as follows:

Substituting (2.36) into (2.35), we easily get sin(𝑞 1 − 𝜑) = 𝑑 3 −𝑑 2 −𝑑 4

For Equation (2.39) to have real solutions, the following condition must be satisfied:

The condition (2.40) depends on the robot's configuration and the trajectory of the end- effector Assuming this condition is satisfied, then Equation (2.39) has two real solutions, which are:

From there, we deduce two solutions for q 1

Once q 1 has been determined from Equation (2.29), it can be easily deduced from equation (2.29) that

⇒ 𝑞 5 = ±arccos (𝑎 𝑥 𝑠 1 − 𝑎 𝑦 𝑐 1 ) (2.42) For each value of q 1 we you obtain two values for q 5; therefore, we have a total of 4 solutions for q 5, as follows:

For each pair of values q 1, q 5 we obtain2 solutions for q 6 Thus, we will have a total of 8 solutions for q 6, as follows:

On the other hand, from Equation (2.31) we have

For each value of q 1, we obtain one value for q 234 Thus, we have 2 solutions for q 234 as follows:

From (2.32) and (2.33), we can deduce

Note : For each set of values of q 1, q 234 và q 5, we have one pair of values for D 1 and D 2 Therefore, we have 4 pairs of values for D 1 và D 2 as follows:

By squaring both sides of Equations in (2.50) and then summing them up, we obtain:

For each pair of values D 1 and D 2, we have 2 solutions for q 3; or in other words, for each set of values q 1, q 234 and q 5, we havee 2 solutions for q 3 Therefore, we have a total of 8 solutions for q 3, as follows:

The system (2.54) is a system of linear algebraic equations with the variables c 2 and s 2 The solutions to this system have the form:

It's easy to see that the variables ∆, ∆ 𝑠2 , ∆ 𝑐2 depend on 𝐷 1 , 𝐷 2 , 𝑞 3 Therefore, we have sets of values for ∆, ∆ 𝑠2 , ∆ 𝑐2 as follows:

For each set of values of ∆, ∆ 𝑠2 , ∆ 𝑐2 , we have one solution for 𝑞 2 Therefore, we will have a total of 8 solutions for 𝑞 2 , as follows:

Once we have determined q 2 and q 3, we can easily deduce the form of q 4 from Equation (2.45) as follows:

For each pair of values q 2 and q 3, we have one value for q 4 Therefore, we will have a total of 8 values for q 4, as follows:

So, for the inverse dynamics problem, when finding solutions using the analytical method, you will obtain 8 sets of solutions for the joint variables q 1 , q 2, q 3, q 4, q 5, and q 6, as provided in the table below:

Table 2 2 Analytical solutions of the inverse dynamics problem

- In the formulas above provided, the following symbols are used:

- If 𝑞 5 = 0 ⇒ 𝑠 5 = 0, then q 6 can take any value, and in this case, the system has an infinite number of solutions

Specifications of the UR3 robot

The UR3 collaborative robot, according to the technical specifications provided on the Universal Robots website [63], is a small tabletop collaborative robot suitable for bulb light assembly tasks and building automation scenarios on a tabletop This compact tabletop cobot weighs only 24.3 lbs (11 kg) but has a payload capacity of up to 6.6 lbs (3 kg) It can rotate ±360 degrees on all wrist joints and has unlimited rotation on the final joint The details regarding the angle limits, joint speeds, and the robot's workspace are described in detail in Figures 2.8 and 2.9

Figure 2 8 The angle limits and joint speeds of the UR3 robot's joints

Figure 2 9 Vertical Projection (Left) and Side Projection (Right) of the workspace of the

The simulation model, which forms the digital space within the digital twin, is a dynamic environment constructed by integrating 3D computer-aided design (CAD) objects into Tecnomatix Process Simulate software According to Tao [44], the virtual model is composed of four layers: geometry, involving the creation of 3D CAD objects; physical location, determining the positioning of CAD objects within the scene; behavior, encompassing robotic kinetics; and rules, detailing the sequence of an assembly process The Siemens Support Center hosts 3D kinetic CAD objects of the robot within its online library for accessibility

Conclusion of Chapter 2

In this chapter, the assembly system for lightbulbs using the UR3 robot has been described in detail, including each device and the function of each device within the system Each device is used to perform a specific function, such as transporting bulb sockets and bulb caps to the correct positions, ensuring precise assembly, and completing the final product

Subsequently, the operation cycle of the system has also been described, including the cycles of supplying bulb sockets and caps, completing the assembly process, and the cycle of delivering the finished products to the storage warehouse

The assembly system described here is a typical and commonly encountered system in industrial manufacturing facilities This model is built and used for research purposes and can be fully scalable and applicable in real-world scenarios on a larger scale

At the core of the lightbulb assembly system is the UR3 robot In this chapter, the postgraduate focuses on solving forward and inverse kinematics problems and simulating the motion of the UR3 robot with 6 degrees of freedom This is one of the most fundamental challenges in the analysis and syndissertation of robots Some of the results achieved in this chapter include:

1 Forward kinematics analysis of the UR robot: Solving this problem aims to determine the position, velocity, and acceleration of the robot's joints Additionally, this analysis helps us establish the robot's dynamic equations, which serve as the foundation for solving the inverse kinematics problem later on

2 Inverse kinematics analysis of the UR robot: In this problem, we have provided analytical solutions for the joint variables Finding these analytical solutions simplifies the control problem significantly, making it much easier to address in the future

3 From these analyses, the model of the UR3 robot has been constructed within the Tecnomatix Process Simulate software This model accurately describes the robot's operations as well as its limitations Interactive connections have been established to facilitate communication between the real robot and the virtual robot

APPLICATION OF DIGITAL TWINS IN PATH FINDING FOR ROBOTS

Robot path planning problem

3.1.1 Path planning problem for robot

The problem of finding paths for industrial robots is a crucial element in increasing the efficiency of the entire automation system Path planning for industrial robots involves various algorithms, often created before the robot operates, to determine its motion

Essentially, path planning algorithms determine how an industrial robot's arm should approach a component, how it should manipulate that component, and how it should navigate itself to achieve optimal productivity while avoiding collisions Path planning for industrial robots is an essential component of manufacturing automation systems, ensuring that path planning is accurate, safe, and efficient

This field has attracted the attention of many researchers, and the number of studies in this area has been steadily increasing in recent years

Offline path planning for robots is a technique used to plan robot paths without the robot being in operation This approach allows for precise and safe path planning in advance, ensuring that the robot's movements are optimized for productivity and safety

In most cases, the path planning for robots is completed before their operation, prior to the robot tackling a new task This is typically done in an offline programming environment utilizing realistic simulations of the robot's working conditions In this way, programmers can predict and calculate the automation variables that arise in the working environment and plan the robot's path accurately

Offline programming has rapidly become an essential tool for robot integrators and is a highly sought-after feature for robot users because it significantly reduces the time required to teach a robot a specific path Nowadays, most robot paths are planned using this method The role of appropriate path planning in manufacturing is crucial When robot path planning is done correctly, industrial robots can efficiently perform their subsequent tasks Path planning for robots plays a significant role in the following aspects:

- The accuracy of robots: The path of the robot needs to be meticulously planned so that it can efficiently handle a task with minimal or no errors

- Task repeatability: Once the robot's path is clearly defined, it can repeat the same task thousands of times without any changes, thereby increasing throughput

- Product quality: When products are manufactured with high accuracy and repeatability, there are fewer errors and higher overall quality, leading to a higher- quality end product

Robot path planning is extremely important to enable the robot to carry out its assigned tasks effectively, and in this way, it plays a crucial role in the manufacturing process [65]

3.1.2 End-effector motion of the robot

Principles of robot motion control

The principles of controlling the motion of industrial robots are fundamental and essential There are two key aspects when it comes to the motion of industrial robots: where the robot is heading and how it gets there The target position indicates the location to which the robot needs to move The target position is programmed into the robot's system, and the robot approaches the target position multiple times Since the primary objective of industrial robots is achieving a specific location, it can be said that industrial robots perform position control In the case of industrial robots, the process of recording the target position is often referred to as teaching or programming In the case of UR robots, the target position is called a waypoint and can be taught using manual control in Freedrive mode or gently moved using the Teach Pendant [63]

Figure 3 1 Target position and trajectory

The trajectory defines how the robot reaches the target position Robots can move along a straight path or follow a curved path Generally, the robot's trajectory depends on the workspace it is operating in In the case of UR robots, the trajectory is determined using the

"Move" command on the Teach Pendant There are four available Move commands for UR robots: MoveJ, MoveL, MoveP, and MoveC In this dissertation, the UR3 robot uses only two motion commands, MoveL and MoveJ, for its movements

End-effector point in linear space

The Tool Center Point (TCP)

When operating a robot in linear space, it is important to determine the position and orientation of the Tool Center Point (TCP) Assuming that a tool is attached to the end of the robot, referred to as the tool flange, to perform useful tasks, the TCP must be controlled within linear space When the deviation of the TCP is defined with respect to the tool flange, the robot's TCP position can be calculated using kinematics It is crucial to determine a specific TCP offset for applications that require linear motion control [63]

Figure 3 2 Tool Center Point (TCP) of the gripper

Figure 3 3 Comparison of toolpath with and without TCP

Base coordinate system and tool

The coordinate system of the Tool Center Point (TCP) is defined in relation to the base coordinate system, which is a Cartesian coordinate system with its origin at the center of the robot's base Since the robot is mounted in a fixed position, the base coordinate system is also referred to as the absolute coordinate system or the world coordinate system In UR robots, the Cartesian coordinate system is a feature, with the base feature fixed, where the Y-axis is aligned with the robot's cable and the Z-axis points upward [63]

When the TCP has a position and orientation, it also defines its own coordinate system The tool coordinate system simplifies programming and enhances accuracy In UR robots, the Tool feature is defined with its origin at the center of the current TCP and changes as the robot moves

Figure 3 4 Base coordinate system and coordinate system attached to the tool

The A* pathfinding algorithm

One of the methods for finding a path is the A* algorithm A* constructs all possible routes from the starting point until it finds a path that reaches the destination However, like all informed search algorithms, it only constructs routes that "seem" to lead toward the goal

To determine which routes are likely to lead to the destination, A* uses a "heuristic estimate" of the distance from any given point to the goal In the case of pathfinding, this estimate can be the Euclidean distance - an approximation commonly used for measuring distances in transportation routes

The key difference with A* compared to best-first search is that it also takes into account the distance traveled so far This makes A* "complete" and "optimal", meaning that A* will always find the shortest path if such a path exists

This algorithm generates a solution after receiving input and computing several possible paths A* is defined as a computer science algorithm used in pathfinding using graph traversal (meaning reliable paths drawn from the source to the destination can be traversed) Based on the best-first search, A* can create the path with the lowest cost from the starting point to the desired end When traversing the map, A* compares and selects the path with the lowest cost and keeps track of known paths by using a sorted priority queue to monitor the paths The algorithm is highly accurate because it considers all points on the map It can find the lowest-cost path based on an optimal function The following equation describes the basic principle of the method: f(x) = g(x) + h(x)

In this equation, "X" represents a location on the map; "g(x)" is the total distance from the source point to the current point "X"; "h(x)" is a heuristic function used to calculate the distance from the current position "X" to the desired position By using this method, a robot can find an alternative path when reaching a dead-end location (a location with no further path) and can bypass paths leading to dead-ends when maintaining two lists, CLOSED and OPEN These lists are fundamental features for setting up the A* algorithm; the "CLOSED list" is used to record and store checked positions, while the "OPEN list" is used to record positions adjacent to the computed ones, calculate the distance from the "starting position" to the "destination position," and also store the parent position of each position (used in the final step of the algorithm for planning the path from the destination position back to the starting position); thus, an optimal path is found The flowchart of the A* algorithm is displayed below [66]:

Figure 3 5 The flowchart of the A* algorithm

The enhanced method's initial improvement involves pre-planning a local path from the current node to the target node, followed by searching the vicinity of the current node If safe and free of collisions, this local path is directly traversed Secondly, the method utilizes post-processing to optimize the resultant path by straightening the local path, thereby reducing both the number and length of local paths required

In this algorithm, the query phase of the probabilistic motion planning involves path planning based on the improved A* algorithm [67, 68] There are two stages in probabilistic motion planning: the first stage is the preprocessing stage, and the second stage is the query stage In the first stage, a random generation of collision-free sample points is carried out within the robot's workspace These points can also be referred to as nodes in the subsequent stage

In this algorithm, the local path planning then constructs a safe and collision-free local path between these points To validate the path's feasibility and collision avoidance, plans are mapped to the robot's configuration space by the local path planning, and this is done through shared space constraints (such as velocity and acceleration, energy optimization) Therefore, collision-free sample points and safe local paths are components of the probabilistic roadmap In the subsequent stage, with the application of the improved A* algorithm, the probabilistic motion planning generates a path that searches and obtains a safe path for the robot's motion connecting the initial node S (Start point) and the target node G (Goal point) In this research, configuration space constraints are defined by parameters (such as angular range, velocity range, acceleration, velocity deformation, and optimal inverse kinematics solution) to construct the probability map

In the improved A* algorithm, the points that the robot passes through, identified by the traditional A* algorithm, undergo a calculation The algorithm assesses local connections to the subsequent points to determine if they traverse obstacles If a connection does not intersect with an obstacle, the intermediate point is skipped This process effectively reduces the number of points the robot needs to traverse while ensuring a correct path from the starting point to the destination as per the original problem statement

The flowchart of the improved A* algorithm (Figure 3.6) is described as follows [69]:

Figure 3 6 The flowchart of the improved A* algorithm

Step 1: Assign i to 1 and j to n − 1, where i and j are index values of the robot's traversed points currently under consideration Optimize the path from the starting point p1 to the ending point pn in the CLOSED list

Step 2: Set all local paths between point pi and pj, where j is greater than i + 1 and less than n − 1

Step 3: Check if local paths encounter collisions with obstacles If all local paths result in collisions, proceed to Step 4 Otherwise, move to Step 5

Step 4: Save the local path between point pi and pi+1, then increment i by 1 (i = i + 1) Step 5: Save the local path containing node pj with the largest j, replace i + 1 with j − 1, and set i = j

Step 6: Check if i equals n − 1 (meaning point i is close to the last point); if yes, proceed to Step 7 If not, go back to Step 2

Step 7: Connect the points in the locally optimized path previously saved, resulting in a sequential connection of the globally optimized path

The optimization results obtained by to the improved A* algorithm compared to the original A* algorithm are shown in Figures 3.7-3.10

Figure 3 7 A simple example of a robot task

Figure 3 8 A* algorithm-based path planning

Figure 3 9 Optimal result of the first step on the left, the second step on the right

Figure 3 10 The optimal result of the final step

3.3 Application combining digital twins and A* algorithm in robot pathfinding

The proposed method has been implemented on the assembly system using the UR3 robot The experimental setup involves mounting the UR3 robot on a stand and placing it on a table The UR3 robot has 6 degrees of freedom, a payload capacity of 3 kg, and a reach of 500 mm The assembly components are transferred from the previous station, where additional parts are installed, and the completed assembly unit is then transferred to the next station

The UR3 robot first grips a lamp socket to place it into a stamped hole, then picks up a lamp cap to insert it into the same hole Lamp caps are supplied through a conveyor system, whereas lamp sockets are arranged within a pallet

Once the stamping cylinder is lowered, applying a press-fit force to join the socket with the cap, the UR3 robot proceeds to pick up the completed product and position it onto a conveyor for transfer to the warehouse Figure 3.11 presents an actual image of the complete assembly system, while the sequence of steps is visually depicted in Figure 3.12

Figure 3 11 An actual image of the complete lightbulb assembly system

The workstation incorporates various parts and components generated as 3D objects, which are subsequently brought into the Tecnomatix environment Tecnomatix has the capability to import CAD data in the JT (Jupiter Tessellation) format

When the system operates, it accomplishes a total of 7 tasks The Robot is responsible for executing 6 tasks (specifically tasks 1 through 4 and 6 through 7), while the stamping cylinder handles 1 task, specifically task 5 Figure 3.12 illustrates these tasks, showcasing the robot missions along with their start and end points, defining their trajectories

Application of combining the digital twin and improved A* algorithm in

3.4.1 Using the digital twin method

Consider the moving distance of the UR3 robot when it transports (i.e., picks up and places on) an assembled product (i.e., a bulb) from the stamped hole to the conveyor belt for warehouse The obstacle herein is the stamping cylinder More obstacles are added when measuring the robotic moving time with the digital twin, A* algorithm and improved A* algorithm applied

Digital twins are used for robotic path planning The collision detection feature in Technomatix software is used to find a suitable path for robotic movement

The robotic path planning was found by the digital twin method as shown in Figure 3.16

Figure 3 16 Robotic path found by the digital twin method

Coordinate parameters and durations for robotic movement corresponding to the acceleration speed 500-800-1200 mm/s 2 and the velocity speed 250-500 mm/s at 50-mm/s steps are displayed in the following table

Table 3 3 Coordinate parameters (A) and durations (B) for robotic movement according to AA1F1F x y z

Case 1A: The robotic path planning was found by the A* algorithm as shown in Figure

3.17 (in the left side) as ABCDEF, we have the following data (Table 3.4)

Table 3 4 Coordinate parameters (A) and durations (B) for robotic movement according to ABCDEF x y z

(mm/s) AB BC CD DE EF Total

Case 1B: Using the A * improved algorithm for robotic path planning, we have the robotic path as ACDF (Figure 3.17 in the right side) This path is 2 points shorter than that obtained by the original A* algorithm We have the durations for robotic movement obtained by the improved A* algorithm as follows (Table 3.5)

Figure 3 17 Robotic path found by the original A* algorithm (the left) and by the improved A* algorithm (the right)

Table 3 5 Coordinate parameters (A) and durations (B) for robotic movement according to ACDF x y z

V (mm/s) AC CD DF Time (s)

3.4.3 Adding obstacles with the same height

Case 2A: adding a 30-mm width obstacle with the same height (Figure 3.18), we have the following results (Table 3.6)

Figure 3 18 Robotic path found by the improved A* algorithm when a 30-mm obstacle added

Table 3 6 Coordinate parameters (A) and durations (B) for robotic movement according to ACD1F x y z

Case 2B: Adding a 50-mm width obstacle with the same height (Figure 3.19), we have the following results (Table 3.7)

Figure 3 19 Robotic path found by the improved A* algorithm when a 50-mm obstacle added

Table 3 7 Coordinate parameters (A) and durations (B) for robotic movement according to ACD2F

3.4.4 Adding obstacles with varying heights

Case 3: Placing consecutively pairs of obstacles 1-2, 3-4, 5-6 in a 50-mm decreasing order of height as shown in Figures 3.20 and 3.21, we have the following results (Table 3.8): x y z

A (mm/s 2 ) V (mm/s) AC CD D2F Time (s) %

Figure 3 20 Real image of the pairs of obstacles

Figure 3 21 Representation of the pairs of obstacles

Measuring the duration for robotic movement with an increasing number of passing points from D3 to D8, we have the following results

Table 3 8 Coordinate parameters (A) and durations (B) for robotic movement when more pairs of obstacles added in a 50-mm decreasing order of height x y z

The experiment investigated robotic movement parameters based on acceleration values of 500-800-1200 mm/s² and velocities ranging from 250 mm/s to 500 mm/s with intervals of 50 mm/s Three scenarios were explored: (1) A* and improved A* algorithms; (2) improved A* algorithm with added obstacles of the same height; (3) Improved A* algorithm with added obstacles of varying heights Measurement results, presented in Tables 3.3 to 3.8, include coordinates in the robot's spatial movement and time taken for the robot to move The last column in each table illustrates the percentage increase (positive values) or decrease (negative values) in movement time when comparing the A* and improved A* algorithms with digital twin method

Consider Case 1 when the A* algorithm (1A) and improved A* algorithm (1B) were used It is shown that the robotic moving time could be shorter or longer when A* algorithm used in place of digital twin The smallest difference is about 3.544 s (-11.93%) corresponding to a velocity of 250 mm/s and an acceleration of 1200 mm/s 2 ; the largest difference is about 4.456 s (5.24%) corresponding to a velocity of 450 mm/s and an acceleration of 500 mm/s 2 It obviously means that the A* algorithm is not always better than the digital twin We see that in the case of a few obstacles, the duration for robotic movement obtained by the improved A* algorithm is smaller than that obtained by digital twin method In contrast the improved A* algorithm is always better than digital twin as the average robotic moving time reduced by -20.43% ÷ -22.07%

Consider Case 2 when obstacles with constant height (case 2A: an obstacle with 30-mm larger in width and case 2B: an obstacle with 50-mm larger in width) were added the improved A* algorithm helped reduce the average robotic moving time by -18.07% and - 16.44%, respectively

Consider Case 3 when obstacles with varying dimensions were added in pair It is shown that for obstacles with < 50 mm in height the improved A* algorithm increased the robotic moving time in most cases In case 3, when the number of obstacles increases with varying heights, leading to an increase in the number of passing points We find that starting at point D4, the duration for robotic movement obtained by digital twin method is getting shorter with speeds of 350 mm/s or more

When the obstacles 3-4 with < 50 mm in height were added the A* algorithm increased the robotic moving time over the range of velocity and acceleration under study When the obstacles 5-6 with < 50 mm in height were also added the improved A* algorithm further increased the average robotic moving time by 23.9% and 41.36% respectively It implies that the digital twin is better than the improved A* algorithm when obstacle with varying heights used; whereas the reverse is true when obstacles with constant height used.

Conclusion of Chapter 3

In this chapter, the postgraduate has applied a combination of methods to find paths for robots Experiments on pathfinding coordination using the combination of the A* algorithm, improved A* algorithm, and the digital twin approach have been conducted on

Page 78 the UR3 robot in the lightbulb assembly system In these experiments, the robot's motion time was measured using the digital twin method, A* algorithm, and improved A* algorithm under different obstacle scenarios, with constant and variable obstacle heights corresponding to accelerations of 500 mm/s², 800 mm/s², and 1200 mm/s² For each acceleration, a range of velocities from 250 mm/s to 500 mm/s with a 50 mm/s increment was investigated

Our results show that the applicability of improved A* algorithm and digital twin method is dependent upon the robotic speed, acceleration, and number of passing points

Although the improved A* algorithm is better than the digital twin method in terms of shortening robotic moving distance, the influence of robotic velocity and acceleration on its inertia when changing direction of movement must be taken into account It results in the fact that the robotic moving time could get shorter by the improved A* algorithm in the case of adding obstacles with constant height or by the digital twin method in the case of adding obstacles with varying heights Thus, the application of a robotic path planning method needs to adapt to the characteristics and a number of obstacles in reality

APPLICATION OF DIGITAL TWINS IN HUMAN-ROBOT

Theoretical basis

4.1.1 Collaboration between humans and robots

Nowadays, the construction of automation systems in both manufacturing and daily life is an inevitable trend The desire to achieve full automation using robots, replacing humans in factories, has been around for a long time but is often considered impractical in many real-world applications due to numerous technical challenges Industrial robots, with their high precision and repeatability, excel at handling relatively complex manufacturing tasks and performing hazardous and dangerous operations However, industrial robots are typically heavy, less flexible, and pose safety risks to humans As a result, contemporary production processes often tend to be fully automated by machines or semi-automated This approach can lead to significant costs associated with research, machinery investment, operation, and maintenance In fully automated production lines, every task must follow a

Page 80 standardized procedure, and even minor errors during operation can have far-reaching consequences for the entire system due to the lack of flexibility Constructing an intelligent and flexible robot system that can adapt to unexpected situations like humans is currently considered unfeasible due to technological limitations and the cost of investment compared to the benefits it would bring

On the other hand, the manual production model is characterized by its adaptability and high variability Thanks to their flexibility and dexterity, humans can easily handle complex tasks that robots either cannot perform or would require significant new resources to achieve, relying on their experience and skills Building and restructuring production processes in a manual system are also simpler and less costly compared to a fully automated system Nevertheless, in today's development trend, where the value of human labor is increasingly emphasized, labor costs are becoming scarce and expensive Furthermore, some physically demanding and hazardous tasks can impact the health and lives of workers Operating entirely through manual labor may become outdated and less efficient over time, especially on a large scale The phenomenon of bottlenecks in the production process often arises because workers may lose their ability to concentrate, and productivity decreases over time Human errors can lead to uneven product quality

A solution and an inevitable trend have been proposed, which is the development of the Human-Robot Collaboration (HRC) model [70] This approach aims to overcome production challenges by combining the strength and precision of robots with the creativity, thinking, and decision-making abilities of humans With the advancement of robotics technology today, robots and humans can work safely together, interact, and communicate in a shared space without the need for physical barriers Collaborative robots, also known as cobots, have been developed to replace humans in physically demanding, hazardous, repetitive, or monotonous tasks that are prone to errors when performed by humans These collaborative robots are highly compact and can be easily deployed, installed, and programmed rapidly

The concept of human-robot collaboration is elaborated upon in detail in document [70] Researchers have identified the characteristics of collaborative models and outlined development strategies and research directions We have used it as a foundation to guide our research in this area Initial research on collaboration focused on the safety of human co-workers [71, 72], gradually evolving into various forms of collaborative research The work of authors [73] discusses optimizing the number of robots relative to the number of human workers based on individual characteristics and the compatibility of robot clusters One research direction that has garnered significant attention from many scientists is the optimization of ergonomics As the value of human labor continues to rise, making labor costs scarcer and more expensive, there is a growing need to focus on worker health and labor regeneration Research in this direction involves examining ergonomic tasks corresponding to each step in a task and assigning them based on the physiological characteristics of humans or robots [74, 75] They combine predictive models with graph search algorithms that incorporate robot assistance in physically demanding tasks to address issues related to musculoskeletal problems Similar to the aforementioned studies, other researchers [76] optimize assembly processes with goals related to cost, time, and

Page 81 consideration of robot characteristics during the assembly process This includes factors like tool changes, orientation changes, and end-effector motion

There have been numerous methods developed to optimize production planning in human-robot collaboration These methods often fall under the category of evolutionary computation The authors have used algorithms such as Bee Colony Optimization to address the problem of minimizing human labor energy consumption during collaboration in assembly-disassembly lines [77] Feasible solutions for the path-finding problem have been explored using swarm intelligence algorithms [78] Two common types of human- robot collaboration in production are assembly and disassembly, with a focus on assembly lines in this research The assembly problem on production lines is a common and complex issue that is frequently addressed in manufacturing plants

The Genetic Algorithm (GA) was initially proposed by D.E Goldberg and later developed by L Davis and Z Michalewicz Genetic

Algorithm is a computer science technique used to find suitable solutions for combinatorial optimization problems [79] It is a branch of evolutionary algorithms that apply principles of evolution, such as genetic operations, mutation, natural selection, and crossover

Genetic Algorithms (GAs) utilize the process of evolution found in nature to solve real-world optimization problems Starting from a population of initial candidate solutions,

GAs iteratively evolve and apply mutation operators to generate a new set of solutions with improved fitness The final solution is an approximate optimal solution The algorithm's flowchart is shown in Figure 4.1

Crossover: The process of creating new chromosomes based on two (or more) parental chromosomes The new chromosome inherits characteristics from both parents

Mutation: A change at one (or multiple) gene positions on a chromosome compared to the original structure, resulting in a new chromosome Mutations occur less frequently than crossovers and can create new individuals that are either worse or better

Genetic algorithms have proven their effectiveness in studies related to human-robot collaboration [80-85] Part of the evolutionary computation category, this algorithm draws from two established biological concepts: genetics and evolution By emulating genetic mechanisms observed in biology, this approach offers approximate solutions to optimization problems that conventional methods struggle to solve [86]

Selection methods in genetic algorithms

There are several selection methods used in genetic algorithms, such as:

Random selection is the simplest method of selection Random selection uses the random function in programming to choose individuals randomly from the population This selection is not based on any fitness information of the individuals Therefore, this method is less efficient and is often less utilized, especially in problems with higher complexity and small solution spaces

The Ranking Selection method, introduced by Baker in 1985, is used in genetic algorithms The idea behind this method is to rank the population from the best to the worst individuals and then assign the number of copies that each individual will receive based on a non-decreasing rule

Tournament Selection is another method that evaluates selection based on the fitness function f The idea here is to select the best individual within a group, known as the tournament size, from the population This strategy primarily involves comparing the fitness values of the individuals

The process of Tournament Selection can be described in two steps:

Step 1: Randomly select a certain number of individuals from the population to participate in a tournament Compare and choose the individual with the highest fitness value among the selected individuals

Roulette Wheel Selection is the most commonly used method in genetic algorithms

This method follows the principle of simulating a roulette wheel game In the game, a wheel is spun, and when it stops, a pointer points to a reward section While we cannot predict the exact location the pointer will land on, we can still evaluate the probability of selecting different regions The probability of selection is directly proportional to the central angle's size of that region The larger the central angle, the higher the probability that the pointer will land in that region

Similarly, in genetic algorithms, the entire wheel represents the population and is divided into segments by individuals Each segment on the wheel represents an individual The

Page 83 proportion of each segment is determined by the ratio of the individual's fitness value to the total fitness value of the population This is illustrated in the diagram in Figure 4.2

Figure 4 2 A chart illustrating the Roulette selection method

The steps to implement the Roulette Wheel Selection strategy are as follows:

Step 1: Calculate the fitness value (f) of each individual in the population Calculate the total fitness value of the population

Step 2: Evaluate the fitness ratio of each individual compared to the total fitness value of the population

Where: n is the number of individuals in the population

Ps is the selection probability

𝑎 𝑖 is the i th individual in the population

Applying a combination of the digital twin method and genetic algorithm in

4.2.1 Overall framework diagram of the digital twin method for human-robot collaboration

Figure 4 3 Overall framework diagram of the digital twin method for human-robot collaboration

Figure 4.3 showcases the hierarchical operational framework within the digital twin structure for facilitating the effective design, development, and functioning of HRC (human-robot collaboration) systems [53] The digital twin framework consists of two interconnected environments, namely the physical environment and the virtual environment The physical environment constitutes the actual production system in the real world, encompassing humans, robots, and associated production machinery Conversely, the virtual environment refers to a computer-simulated space Every component within the physical system corresponds and synchronizes with its digital representation in the virtual environment This synchronization ensures that each element in the virtual simulation mirrors the operational state of its connected physical object within the production system The proposition involves creating a virtual or digital replica of the HRC system during the ideation phase, aiming to enhance the design and development process The digital twin remains consistently updated to reflect all evolutionary alterations and adjustments occurring within the physical system Consequently, the simulation initiated during the ideation phase undergoes continual enhancement in terms of its content and integration with the physical setup Throughout operations, at every production switch, the digital space swiftly progresses through a comprehensive runtime cycle, facilitating the optimization of production management decisions Since the digital twin framework supports activities in

Page 87 the design, development, and operation phases, the digital twin's activities may vary in each stage of the lifecycle

4.2.2 Description of the human-robot collaboration system

In this study, the experimental model revolves around a scaled-down lightbulb assembly setup, comprising a workstation equipped with both human and robot manipulators The assembly process is executed by a UR-3 robot manipulator, possessing six degrees of freedom, capable of handling up to 3 kg, and with a reach extending to 500 mm The workstation undertakes tasks such as receiving a sub-assembly from the preceding station, mounting supplementary components, and subsequently transferring the sub-assembly to the succeeding station

The UR3 robot carries out the task of retrieving sockets from the pallet and inserting them into the stamped hole It then proceeds to pick up lightbulbs from a conveyor belt and place them into the same stamped hole While the lightbulbs are conveyed via a belt, the sockets are stored within a pallet Following the application of force by a stamping cylinder to secure the socket to the bulb, the UR3 robot retrieves the final product and deposits it onto a conveyor belt for transfer to the warehouse Figure 4.4 showcases both an authentic image of the complete assembly system and a schematic diagram delineating the system's layout

At the assembly workstation, the worker is involved in three primary tasks: (i) remaining stationed at the home position; (ii) transporting the finished product to the warehouse; (iii) restocking the pallet with sockets when their supply is low and replenishing bulbs on the conveyor belt before they run out This collaborative effort between human and robot ensures a continuous and uninterrupted operation by maintaining an adequate supply of materials The finished product is thus delivered to the warehouse promptly, preventing congestion and system halts

Figure 4 4 Real image (on the left) and schematic diagram (on the right) of the miniature lightbulb assembly system

The challenge in the miniature lightbulb assembly system is to minimize worker movements while guaranteeing uninterrupted robot operation by ensuring a consistent supply of sockets and lightbulb caps

At the initial time (t=0), assume that the worker is standing at the Home position There are B lightbulb sockets on the pallet, and there are C lightbulb caps on the conveyor Through various experiments, the values are taken as averages of multiple trial runs and rounded to the nearest second It is observed that the total time for the movement activity follows the formula:

Where 𝑇 𝑐 is the total time for the worker to move for supplying lightbulb caps 𝑇 𝑀 is the time taken by the worker to move 𝑇𝑐 𝑖 is the time for supplying lightbulb caps, with i being the number of caps The worst-case scenario involves the worker moving, capping all available sockets, and then returning, with a total time of 26 seconds

Similarly, we have the time required for moving and supplying lightbulb sockets, which can be calculated as follows:"

Based on the experimental data for the UR3 robot model in the assembly of lightbulbs, with a production trial of 100 lightbulbs, the following information is provided:

Distance for moving and supplying lightbulb caps = 5.4 (m)

Distance for moving and supplying lightbulb sockets = 5.4 (m)

Robot linear speed: 300 mm/s; acceleration 1300 mm/𝑠 2

Robot angular speed: 75 rad/s; 100 rad/𝑠 2

According to the experimental data, the time it takes for a human to complete the assembly of one lightbulb is 30 seconds

4.2.3 Application of digital twins in human-robot collaboration

The digital twin, employing a dynamic simulation model, is developed using Tecnomatix Process Simulate software It includes design objects supported by 3D computer-aided design (3D CAD) models imported from the online library of the Siemens Support Center The model is structured into four layers—geometry, physics, behavior, and rules—in accordance with Tao's framework [44] Additional components necessary for the workstation are designed as 3D objects in NX and then integrated into the Tecnomatix environment The human simulation process involves generating a digital model of the human worker to assess ergonomics Realistic representations of male and female figures are produced using mesh deformation technology to accurately depict body shapes [52]

The selected models have a height of 1.60 meters, a BMI (Body Mass Index) below 25, and waist-to-hip ratio (for females) is considered

This research explores the use of cameras to monitor the position and presence of humans in the workspace of human-robot collaboration (HRC) to track and analyze the level of interaction between humans and robots, as well as the frequency of these interactions The collected information serves to periodically refine the robot's trajectory by identifying areas frequently accessed by humans Leveraging historical human position data, the simulation autonomously learns and generates robot trajectories, eliminating the need for human intervention in this process

Figure 4.5 displays the representations of an actual human and a robot alongside their digital counterparts within the digital twin The digital model of the system was constructed using Tecnomatix software The highlighted red rectangle in the image denotes potential collision area in the shared workspace between the human and robot

Figure 4 5 The real human and robot (displayed on the left) and their digital representations within Tecnomatix software (featured on the right)

The simulation model records crucial robot positions Upon task definition and assignment, these tasks are simulated within a virtual environment, generating robot trajectories Intermediate positions are automatically determined, ensuring collision avoidance with equipment The resultant paths are saved in an SRC file, which can be uploaded onto the robot In cases of dynamic changes, alterations in robot operations are relayed as override messages to the initial robot program [93]

4.2.4 Application of genetic algorithms in human-robot collaboration

4.2.4.1 Initialization of the initial population

In this research, a chromosome is constructed by encoding the regular working process, where each gene corresponds to a working state within a unit of time This approach not only yields an optimal work plan for humans during collaboration but also specifies what each person should do at a given time

Based on the analysis of a robot's completion time for assembling one bulb, which is 30 seconds, the work plan for humans is divided into corresponding 30-second steps In total, for a production process of 100 bulbs, a human will execute 100 steps Each step contains the corresponding working state of the human The chromosome representation is in the form of a binary vector with a length equal to the number of tasks in the job, which has shown good results [94] Task allocation in the problem [95] uses a chromosome with 2 halves corresponding to defining tasks This is suitable as actions are grouped

A chromosome with double the number of steps in the plan is used, and they are encoded in binary The first half of the chromosome represents the human's moving or standing state, while the second half represents the human's moving direction: either moving to the conveyor or to the pallet The state of each step is determined based on the two corresponding genes in the two halves of the chromosome The gene encoding details on the chromosome are presented in Table 4.1

Table 4 1 Gene encoding on chromosomes Genes on the first half Genes on the second half Status

For example: A random chromosome for a production plan of 100 lightbulbs is depicted in Figure 4.6 The first gene of the chromosome is represented as 1, and its corresponding gene in the second half is 0 Therefore, this gene contains information: the human is moving to the conveyor

The number of genes in the chromosome is equal to the number of steps in the process, so it changes over time for the entire batch The larger the population, the higher the diversity of the chromosome characteristics, making it possible to find the optimal solution sooner However, the number of individuals needs to be balanced with the number of genes and the crossover generation factor; otherwise, it can lead to repeated gene patterns, wasting computational space

Conclusion of Chapter 4

In this chapter, the application of a digital twin in human-robot collaboration has been implemented based on the results of creating a digital twin model of the UR3 robot Specifically, it involves applying digital twin techniques and genetic algorithms to solve the problem of human-robot collaboration First, there is a presentation of the theory of human-robot collaboration and genetic algorithms Next, the practical implementation involves optimizing the robot's path and the quantity of human movements, aiming to maintain adequate materials within the system and ensure smooth operation while optimizing movements for efficiency

The purpose of optimizing the collaborative process is to benefit the human collaborator in the process of working alongside the robot on the production line With the new aspects of the genetic algorithm such as chromosome encoding and improved selection methods, the multi-adaptive genetic algorithm has yielded good results in minimizing the operator's actions

The experiment was conducted on a sample production process of assembling 100 lightbulbs Under the initial conditions, the system had a sufficient supply of materials and a person was in a ready position to work Prior to employing the multi-adaptive genetic algorithm, the individual assembled 100 lightbulbs across 50 cycles, relying on their observational abilities, with information recorded via a camera The average results of the experiment participant were as follows: the average number of lightbulb cap placements was 25.85 times, the average number of socket placements was 21.03 times, and the total number of movements was 46.87 times After running the Matlab software program using the multi-adaptive genetic algorithm for 50 cycles, the average number of screw insertions decreased to 21.52 times The average number of cap placements was 15.02 times, and the total number of movements was 36.54 times As a result, when applying the multi-adaptive genetic algorithm, the number of movements by the operator decreased by approximately 22% The application of digital twins combined with the genetic algorithm significantly increased the efficiency of human-robot collaboration in the lightbulb assembly system

With the topic "Research on Developing Digital Twins-based Application for Industrial

Robots" the dissertation has achieved the following results:

1 Analyzed, evaluated, and built a simulation of the operation of industrial robots, and performed experiments on the UR3 robot in the lightbulb assembly system Constructed a virtual model of the UR3 robot and established communication between the real UR3 robot and the virtual model

2 Studied and developed the A* and Improved A* algorithms in coordination with the dual-task approach for path planning of the UR3 robot in the lightbulb assembly system Conducted experimental measurements to evaluate the robot's motion time in cases with obstacles of constant size and obstacles with variable heights, using different acceleration values of 500 mm/s², 800 mm/s², and 1200 mm/s², corresponding to velocity values ranging from 250 mm/s to 500 mm/s with a step size of 50 mm/s The results demonstrated that the Improved A* algorithm consistently performed better in terms of motion time for the robot in cases with obstacles of constant height, and the dual-task method proved to be more effective in terms of motion time in cases with obstacles of varying heights

3 Studied and developed an application of genetic algorithms combined with numerical optimization for human-robot collaboration, providing a schedule of human activities along with a predefined robot motion trajectory to minimize collisions and reduce human movement while ensuring continuous system operation without interruptions due to a lack of input materials The problem was formulated for the collaboration of humans and UR3 robots in the lightbulb assembly system, aiming to assemble 100 lightbulbs in 50 cycles, with two scenarios: without applying genetic algorithms and with the application of genetic algorithms When the algorithm was applied, after running the software program in Matlab with the multi- objective genetic algorithm for approximately 50 iterations, the number of movements made by the human operator was reduced by approximately 22% The implementation of the dual-task approach combined with genetic algorithms significantly improved the efficiency of human-robot collaboration in the lightbulb assembly system

The dissertation proposes an integrated approach using the digital twin method and A* algorithm for robotic path planning The trajectory obtained is then optimized using the digital twin method combined with the genetic algorithm (GA) to enhance human operation during the assembly of light bulbs The two consecutive and complementary studies effectively address optimization challenges in the light bulb assembly system, resulting in a 22% reduction in human movements while ensuring a smooth system operation and an adequate supply of input materials The application of the digital twin method alongside optimization algorithms like A* and GA for solving pathfinding and human-robot collaboration issues represents a novel and valuable contribution within this dissertation

1 Investigate the impact of the robot's inertia on the characteristics of the robot's motion trajectory, especially at positions with sudden changes in angular velocity, on the total robot travel time This research aims to develop optimal methods in terms of both time and space efficiency in robot operations

2 Improve genetic algorithm-based algorithms for coordinating human-robot activities, focusing on algorithm responsiveness when unexpected obstacles appear during system operation

3 Research on DE (Differential Evolution) and PSO (Particle Swarm Optimization) algorithms to create digital twin - DE or digital twin - PSO hydrid algorithms

1 S Bochert, R Rosen, "Digital twin—the simulation aspect", in Mechatronic Futures

Challenges and Solutions for Mechatronic Systems and their Designers, eds P Hehenberger, D Bradley (2016), Springer International Publishing Switzerland, pp 59-74

2 L.A Hernández, S Hernández (1997), "Application of digital 3D models on urban planning and highway design", WIT Transactions on The Built Environment, Vol

3 G Micheal (2019), "Digital twin: manufacturing excellence through virtual factory replication" [cited 2021 June 23]; Available from: http://www.apriso.com/library/Whitepaper_Dr_Grieves_DigitalTwin_Manufacturi ngExcellence.php

4 K.A Hribernik, L Rabe, K.D Thoben, J Schumacher (2006), "The product avatar as a product-instance-centric information management concept", International

Journal of Product Lifecycle Management, Vol 1, pp 367–379

5 K Hribernik, T Wuest, K.-D Thoben (2013) "Towards Product Avatars

Representing Middle-of-Life Information for Improving Design, Development and Manufacturing Processes", in NEW PROLAMAT 2013, IFIP AICT 411, eds G.L

Kovács and D Kochan, Springer Berlin Heidelberg, pp 85-96

6 J Ríos, J.C Hernandez, M Oliva, F Mas (2015), "Product avatar as digital counterpart of a physical individual product: literature review and implications in an aircraft", Transdisciplinary Lifecycle Analysis of Systems, Vol 2, pp 657–666

7 T Wuest, K Hribernik, K.-D Thoben (2015), "Accessing servitisation potential of

PLM data by applying the product avatar concept", Production Planning & Control,

8 M Shafto, M Conroy, R Doyle, E Glaessgen, C Kemp, J LeMoigne, L Wang

(2012), "Modeling, simulation, information technology & processing roadmap", National Aeronautics and Space Administration, Vol 32, pp 1-38

9 Gartner’s Top 10 strategic technology trends for 2017 [cited 2021 June 23];

Available from: https://www.gartner.com/smarterwithgartner/gartners-top-10- technology-trends-2017/

10 Gartner’s Top 10 strategic technology trends for 2018 [cited 2021 June 23];

Available from: https://www.gartner.com/smarterwithgartner/gartners-top-10- technology-trends-2018

11 Gartner’s Top 10 strategic technology trends for 2019 [cited 2021 June 23];

Available from: https://www.gartner.com/smarterwithgartner/gartners-top-10- technology-trends-2019/

12 M Singh, E Fuenmayor, E.P Hinchy, Y Qiao, N Murray, D Devine (2021),

"Digital Twin: Origin to Future", Applied System Innovation, Vol 4(2), 36

13 GlobalData Thematic Intelligence Digital Twins – Timeline [cited 2021 June 23];

Available from: https://www.verdict.co.uk/digital-twins-timeline/

14 GlobalData Plc, "Digital Twin Market Trends and Analysis by Region, Product and

Service, End-use and Segment Forecast to 2030", [cited 2023 August 25]; Available from: https://www.globaldata.com/store/report/digital-twin-market-analysis/

15 M Liu, S Fang, H Dong, C Xu (2021), "Review of digital twin about concepts, technologies, and industrial applications", Journal of Manufacturing Systems, Vol

16 Y Zheng, S Yang, H Cheng (2019), "An application framework of digital twin and its case study", Journal of Ambient Intelligence and Humanized Computing, Vol

17 M Schluse, J Rossmann (2016), "From simulation to experimentable digital twins:

Simulation-based development and operation of complex technical systems" in 2016

IEEE International Symposium on Systems Engineering (ISSE)

18 T Delbrügger, J Rossmann (2019), "Representing adaptation options in experimentable digital twins of production systems", International Journal of

Computer Integrated Manufacturing, Vol 32(4-5), pp 352-365

19 J Bao, D Guo, J Li, J Zhang (2019), "The modelling and operations for the digital twin in the context of manufacturing", Enterprise Information Systems, Vol 13(4), pp 534-556

20 A.M.M.S Ullah (2019), "Modeling and simulation of complex manufacturing phenomena using sensor signals from the perspective of Industry 4.0", Advanced

21 R Stark, C Fresemann, K Lindow (2019), "Development and operation of Digital

Twins for technical systems and services", CIRP Annals, Vol 68(1), pp 129-132

22 J.D Hochhalter, W.P Leser, J.A Newman, E.H Glaessgen, V.K Gupta, V

Yamakov, S.R Cornell, S.A Willard, G Heber (2014), "Coupling damage-sensing particles to the digitial twin concept", National Aeronautics and Space

23 R Rosen, G von Wichert, G Lo, K.D Bettenhausen (2015), "About The Importance of Autonomy and Digital Twins for the Future of Manufacturing", IFAC-

24 B BrennerV Hummel (2017), "Digital Twin as Enabler for an Innovative Digital

Shopfloor Management System in the ESB Logistics Learning Factory at Reutlingen

- University", Procedia Manufacturing, Vol 9, pp 198-205

25 R Sửderberg, K Wọrmefjord, J.S Carlson, L Lindkvist (2017), "Toward a Digital

Twin for real-time geometry assurance in individualized production", CIRP Annals,

26 M Grieves, J Vickers, "Digital twin: mitigating unpredictable, undesirable emergent behavior in complex systems", in Transdisciplinary perspectives on complex systems, eds F.-J Kahlen, S Flumerfelt, A Alves (2017), Springer International Publishing Switzerland, pp 85-113

27 K Bruynseels, F Santoni de Sio, J van den Hoven (2018), "Digital Twins in Health

Care: Ethical Implications of an Emerging Engineering Paradigm", Vol 9, 31

28 M Schluse, M Priggemeyer, L Atorf, J Rossmann (2018), "Experimentable

Digital Twins—Streamlining Simulation-Based Systems Engineering for Industry 4.0", IEEE Transactions on Industrial Informatics, Vol 14(4), pp 1722-1731

29 J Leng, H Zhang, D Yan, Q Liu, X Chen, D Zhang (2019), "Digital twin-driven manufacturing cyber-physical system for parallel controlling of smart workshop",

Journal of Ambient Intelligence and Humanized Computing, Vol 10(3), pp 1155-

30 W Luo, T Hu, C Zhang, Y Wei (2019), "Digital twin for CNC machine tool: modeling and using strategy", Journal of Ambient Intelligence and Humanized

31 Y He, J Guo, X Zheng (2018), "From Surveillance to Digital Twin: Challenges and Recent Advances of Signal Processing for Industrial Internet of Things", IEEE

Signal Processing Magazine, Vol 35(5), pp 120-129

32 N Nikolakis, K Alexopoulos, E Xanthakis, G Chryssolouris (2019), "The digital twin implementation for linking the virtual representation of human-based production tasks to their physical counterpart in the factory-floor", International

Journal of Computer Integrated Manufacturing, Vol 32(1), pp 1-12

33 J Wang, L Ye, R.X Gao, C Li, L Zhang (2019), "Digital Twin for rotating machinery fault diagnosis in smart manufacturing", International Journal of

34 S KaewunruenQ Lian (2019), "Digital twin aided sustainability-based lifecycle management for railway turnout systems", Journal of Cleaner Production, Vol 228, pp 1537-1551

35 S Kaewunruen, P Rungskunroch, J Welsh (2019), "A Digital-Twin Evaluation of

Net Zero Energy Building for Existing Buildings", Vol 11(1), pp.159

36 S Kaewunruen, N Xu (2018), "Digital Twin for Sustainability Evaluation of

37 Y Xu, Y Sun, X Liu, Y Zheng (2019), "A Digital-Twin-Assisted Fault Diagnosis

Using Deep Transfer Learning", IEEE Access, Vol 7, pp 19990-19999

38 J Liu, H Zhou, X Liu, G Tian, M Wu, L Cao, W Wang (2019), "Dynamic

Evaluation Method of Machining Process Planning Based on Digital Twin", IEEE

39 A.M Madni, C.C Madni, S.D Lucero (2019), "Leveraging Digital Twin

Technology in Model-Based Systems Engineering", Vol 7(1), 7

40 Q Liu, B Liu, G Wang, C Zhang (2019), "A comparative study on digital twin models", AIP Conference Proceedings, Vol 2073, 020091

41 G Fotland, C Haskins, T Rứlvồg (2020), "Trade study to select best alternative for cable and pulley simulation for cranes on offshore vessels", System Engineering,

42 P Wang, M Yang, Y Peng, J Zhu, R Ju, Q Yin (2019), "Sensor Control in Anti-

Submarine Warfare—A Digital Twin and Random Finite Sets Based Approach",

43 B Schleich, N Anwer, L Mathieu, S Wartzack (2017), "Shaping the digital twin for design and production engineering", CIRP Annals, Vol 66(1), pp 141-144

44 F Tao, M Zhang (2017), "Digital Twin Shop-Floor: A New Shop-Floor Paradigm

Towards Smart Manufacturing", IEEE Access, Vol 5, pp 20418-20427

45 T Fei, L Weiran, L Jianhua, L Quiang, Q Ting, H Tianliang, Z Zhinan, X Feng,

X Wenjun, W Junqiang, Z Yingfeng, L Zhenyu, L Hao, C Jiangfeng, Q Qinglin,

Z Meng, Z He, S Fangyuan, H Lirong, Y Wangmin, C Hui (2018), "Digital twin

Page 107 and its potential application exploration", Computer Integrated Manufacturing

46 MarketsandMarkets.com, "Digital Twin Market by Technology, Type (Product,

Process, and System), Application (Predictive Maintenance, and Others), Industry (Aerospace & Defense, Automotive & Transportation, Healthcare, and others), and Geography—Global Forecast to 2026", [cited 2021 June 23]; Available from: https://www.marketsandmarkets.com/Market-Reports/digital-twin-market-

47 W Kritzinger, M Karner, G Traar, J Henjes, W Sihn (2018), "Digital Twin in manufacturing: A categorical literature review and classification", IFAC-

48 C.K Lo, C.H Chen, R.Y Zhong (2021), "A review of digital twin in product design and development", Advanced Engineering Informatics, Vol 48, 101297

49 DLR - Institute of Robotics and Mechatronics, "History of the DLR LWR" [cited

2023 August 25]; Available from: https://www.dlr.de/rm/en/desktopdefault.aspx/tabid-12464/21732_read-44586/

50 A Hentout, M Aouache, A Maoudj, I Akli (2019), "Human–robot interaction in industrial collaborative robotics: a literature review of the decade 2008–2017",

51 S Haddadin, E Croft (2016), "Physical human–robot interaction", Springer

52 A Kolbeinsson, E Lagerstedt, J Lindblom (2019), "Foundation for a classification of collaboration levels for human-robot cooperation in manufacturing", Production

53 A.A Malik, A Bilberg (2018), "Digital twins of human robot collaboration in a production setting", Procedia Manufacturing, Vol 17, pp 278-285

54 H Laaki, Y Miche, K Tammi (2019), "Prototyping a digital twin for real time remote control over mobile networks: Application of remote surgery", IEEE Access,

55 C.-J Liang, W McGee, C Menassa, V Kamat (2020), "Bi-directional communication bridge for state synchronization between digital twin simulations and physical construction robots", in Proceedings of the International Symposium on Automation and Robotics in Construction (IAARC)

56 T XiangRong, Z Yukun, J XinXin (2021), "Improved A-star algorithm for robot path planning in static environment" Journal of Physics: Conference Series IOP

57 S Bratchikov, A Abdullin, G.L Demidova, D.V Lukichev (2021), "Development of digital twin for robotic arm" in 2021 IEEE 19th International Power Electronics and Motion Control Conference (PEMC)"

58 G Garg, V Kuts, G Anbarjafari (2021), "Digital twin for fanuc robots: Industrial robot programming and simulation using virtual reality", Sustainability, Vol 13(18), 10336

59 M Groshev, C Guimarães, J Martín-Pérez, A de la Oliva (2021), "Toward intelligent cyber-physical systems: Digital twin meets artificial intelligence", IEEE

60 S.H Choi, K.-B Park, D.H Roh, J.Y Lee, M Mohammed, Y Ghasemi, H Jeong

(2022), "An integrated mixed reality system for safety-aware human-robot collaboration using deep learning and digital twin generation", Robotics and

61 C Li, P Zheng, S Li, Y Pang, C.K Lee (2022), "AR-assisted digital twin-enabled robot collaborative manufacturing system with human-in-the-loop", Robotics and

62 X Guo, G Peng, Y Meng (2022), "A modified Q-learning algorithm for robot path planning in a digital twin assembly system", The International Journal of Advanced

63 Universal Robot [cited 2022 October 18]; Available from: https://www.universal- robots.com/

64 L.-W Tsai (1999), "Robot Analysis: The mechanics of serial and parallel manipulators", John Wiley & Sons, Inc

65 Robotics Online Marketing Team, "Introduction to Industrial Robot Path Planning"

[cited 2022 October 18]; Available from: https://www.automate.org/blogs/introduction-to-industrial-robot-path-planning

66 L Larsen, J Kim, M Kupke, A Schuster (2017), "Automatic Path Planning of

Industrial Robots Comparing Sampling-based and Computational Intelligence Methods", Procedia Manufacturing, Vol 11, pp 241-248

67 G Sánchez, J.-C Latombe (2002), "On Delaying Collision Checking in PRM

Planning: Application to Multi-Robot Coordination", The International Journal of

68 C.M Clark (2005), "Probabilistic road map sampling strategies for multi-robot motion planning", Robotics and Autonomous Systems, Vol 53(3-4), pp 244-264

69 B Fu, L Chen, Y Zhou, D Zheng, Z Wei, J Dai, H Pan (2018), "An improved A* algorithm for the industrial robot path planning with high success rate and short length", Robotics and Autonomous Systems, Vol 106, pp 26-37

70 E Matheson, R Minto, E.G.G Zampieri, M Faccio, G Rosati (2019), "Human–

Robot Collaboration in Manufacturing Applications: A Review", Robotics, Vol 8(4), 100

71 M.J Rosenstrauch, J Krüger (2017), "Safe human-robot-collaboration-introduction and experiment using ISO/TS 15066" in 2017 3rd International Conference on

Control, Automation and Robotics (ICCAR)

72 A Hanna, K Bengtsson, P.L Gửtvall, M Ekstrửm (2020), "Towards safe human robot collaboration - Risk assessment of intelligent automation" in 25th IEEE

International Conference on Emerging Technologies and Factory Automation, ETFA 2020, Institute of Electrical and Electronics Engineers Inc, pp 424-431

73 R Gervasi, L Mastrogiacomo, F Franceschini (2020), "A conceptual framework to evaluate human-robot collaboration", The International Journal of Advanced

74 M Dalle Mura, G Dini (2022), "Job rotation and human–robot collaboration for enhancing ergonomics in assembly lines by a genetic algorithm", The International

Journal of Advanced Manufacturing Technology, pp.1 -14

75 L.v.d Spaa, M Gienger, T Bates, J Kober (2020), "Predicting and Optimizing

Ergonomics in Physical Human-Robot Cooperation Tasks" in 2020 IEEE

International Conference on Robotics and Automation (ICRA)

76 S Hjorth, D Chrysostomou (2022), "Human–robot collaboration in industrial environments: A literature review on non-destructive disassembly", Robotics and

77 W Xu, Q Tang, J Liu, Z Liu, Z Zhou, D.T Pham (2020), "Disassembly sequence planning using discrete Bees algorithm for human-robot collaboration in remanufacturing", Robotics and Computer-integrated Manufacturing, Vol 62,

78 M Kheder, M Trigui, N Aifaoui (2017), "Optimization of disassembly sequence planning for preventive maintenance", The International Journal of Advanced

79 K Hửschel, V Lakshminarayanan (2019), "Genetic algorithms for lens design: a review", Journal of Optics, Vol 48(1), pp 134-144

80 A Raatz, S Blankemeyer, T Recker, D Pischke, P Nyhuis (2020), "Task scheduling method for HRC workplaces based on capabilities and execution time assumptions for robots", CIRP Annals, Vol 69(1), pp 13-16

81 Y.Y Liau, K Ryu (2020), "Task Allocation in Human-Robot Collaboration (HRC)

Based on Task Characteristics and Agent Capability for Mold Assembly", Procedia

82 N Barathwaj, P Raja, S Gokulraj (2015), "Optimization of assembly line balancing using genetic algorithm", Journal of Central South University, Vol 22(10), pp 3957-3969

83 L Chen, W Su, M Li, M Wu, W Pedrycz, K Hirota (2020), "A population randomization-based multi-objective genetic algorithm for gesture adaptation in human-robot interaction", Science China Information Sciences, Vol 64(1), 112208

84 S Parsa, M Saadat (2021), "Human-robot collaboration disassembly planning for end-of-life product disassembly process", Robotics and Computer-Integrated

85 C Ferreira, G Figueira, P Amorim (2021), "Scheduling Human-Robot Teams in collaborative working cells", International Journal of Production Economics, Vol

86 S Mirjalili (2019), "Genetic algorithm" in Evolutionary Algorithms and Neural networks - Theory and Applications, Springer

87 D.E Goldberg, K Deb, "A Comparative Analysis of Selection Schemes Used in

Genetic Algorithms", in Foundations of Genetic Algorithms, ed G.J.E Rawlins

88 Z Jinghui, H Xiaomin, Z Jun, G Min (2005) "Comparison of Performance between Different Selection Strategies on Simple Genetic Algorithms" in

International Conference on Computational Intelligence for Modelling, Control and

Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06)

89 F Yu, X Fu, H Li, G Dong (2016), "Improved roulette wheel selection-based genetic algorithm for TSP" in 2016 International conference on network and information systems for computers (ICNISC), IEEE

90 N.M Razali, J Geraghty (2011), "Genetic algorithm performance with different selection strategies in solving TSP" in Proceedings of The World Congress on

Engineering, International Association of Engineers Hong Kong, China

91 K Jebari, M Madiafi (2013), "Selection methods for genetic algorithms",

International Journal of Emerging Sciences, Vol 3(4), pp 333-344

92 N.Đ Nghĩa (2013), "Cấu trúc dữ liệu và thuật toán", Hà Nội, Việt Nam, Nhà xuất bản Bách Khoa

93 A Bilberg, A.A Malik (2019), "Digital twin driven human–robot collaborative assembly", CIRP Annals, Vol 68(1), pp 499-502

94 T Bọnziger, A Kunz, K Wegener (2020), "Optimizing human–robot task allocation using a simulation tool based on standardized work descriptions", Journal of

95 Y Liu, S Ji, Z Su, D Guo (2019), "Multi-objective AGV scheduling in an automatic sorting system of an unmanned (intelligent) warehouse by using two adaptive genetic algorithms and a multi-adaptive genetic algorithm", PloS one, Vol 14(12), e0226161

96 A Konak, D.W Coit, A.E Smith (2006), "Multi-objective optimization using genetic algorithms: A tutorial", Reliability Engineering & System Safety, Vol 91(9), pp 992-1007.