Solving Clustering and Allocation Problems of Human-Robot Collaboration in Smart Industry 5.0 Applications using FIS-GRA Integration-Based Multi-Objective Programming Model

Due to rapid technological advancements in recent decades, the integration of robots alongside humans in manufacturing has significantly expanded. Beyond simply replacing workers in traditional roles, robots now actively partner with humans to complete tasks. However, successful collaboration between humans and robots requires careful consideration of several crucial factors. This study introduces an efficient approach to collaboratively assigning robots, workers, and tasks. The methodology incorporates a fuzzy inference system and grey relational analysis, integrating two multi-objective programming models as assignment tools. A real case study demonstrates the application of this approach, revealing its superior effectiveness compared to conventional assignment methods.


INTRODUCTION
Engineers have been steering manufacturing models towards Industry 5.0 in the last decade, highlighting a shift towards enhanced collaboration between humans and robots.This differs from the Industry 4.0 era, where technologies like the Internet of Things (IoT) [1], Big Data, and Artificial Intelligence (AI) were harnessed to advance production processes.In Industry 4.0, robots assumed a central role throughout production, akin to the use of "Traditional industrial robots".However, Industry 5.0 introduces a novel approach.It revolves around crafting production processes with a human-centric design [2].This involves fostering harmonious collaboration between humans and robots throughout production, ushering in a newfound equilibrium between human ingenuity and technological prowess [3].The concept of Human-Robot Collaboration (HRC) originated in 1996, a time when industrial robots had gained widespread popularity.This concept involved a redefinition of the term "robot" itself.The emergence of "Collaborative robots" or "Cobots" was a pivotal aspect of this shift [4,5].
The use of traditional industrial robots is fraught with limitations, including the inability to interact with humans and a lack of flexibility in application.These constraints render traditional robots ill-suited for adapting to small-lot production scenarios.However, the introduction of collaborative robots into the industrial landscape addresses these limitations by offering support for a diverse range of production characteristics.Collaborative robots are optimized for small production lots, providing the flexibility and agility required for rapid job changes [1,6,7].The key to integrating collaborative robots into human workflows lies in leveraging the physical attributes of robots, such as precision, repeatability, and strength, alongside human cognitive abilities like problemsolving, quick decision-making, and visual perception [8,9].This collaborative approach yields numerous benefits in the production process, including the maintenance of production standards, mitigation of risks associated with hazardous jobs, and the alleviation of ergonomic issues linked to prolonged heavy lifting-issues that lead to fatigue and reduced work efficiency [10].Furthermore, the introduction of collaborative robots contributes to the overall improvement of the working environment for humans [11].
Integrating collaborative robots into production necessitates careful planning for effective and safe cooperation between humans and robots.This planning involves a multifaceted approach, considering various critical aspects.First and foremost, it requires an assessment of the jobs assigned to each robot, taking into consideration the intricacy and nature of the work, the tools employed, material properties, and component availability [12,13].The selection of robots tailored to the requirements of each specific job is crucial [7].This involves evaluating the capabilities of robots to ensure they are suitable for the jobs at hand.Efficiency and the quality of a robot's work are paramount considerations during this selection process [14,15].Furthermore, preparing and modifying the work area to facilitate human-robot collaboration is imperative.This includes creating a safe and conducive space for both humans and robots to operate harmoniously [6,16,17].Additionally, comprehensive training programs are essential for workers working alongside robots.These programs equip them with the necessary skills for collaborative work and proficient handling of robotic technologies [6,11,18].Establishing a robust framework for collaboration is a key component of the planning process.This framework delineates clear roles and responsibilities for all parties involved in the production process [19].Regular inspection and evaluation of the collaborative efforts are integral to ensure that the production process aligns with planned objectives.This thorough planning and evaluation process is critical for the seamless integration and success of human-robot collaboration in the production environment [12,16,20,21].
In the realm of research on human-robot interaction, the delegation of jobs holds paramount importance in the production process.However, traditional assignment methods fall short of supporting efficient human-robot collaborative manufacturing processes [22,23].The inadequacy arises from the fact that the traditional approach typically considers the interaction between two resources similar to conventional scenarios [19,[24][25][26][27][28][29].In the contemporary workspace, collaborative robots have been introduced at each workstation, adding an extra number of resources.This implies that each workstation now involves not only workers and jobs but also collaborative robots.Consequently, a holistic approach is needed, considering the seamless operation and coordination of all three resources: type of work, collaborative robots, and workers at each station [5].The novel perspective involves a comprehensive consideration of all resources within each workstation, delineating the intricate relationships between the types of work, collaborative robots, and workers responsible for control duties.This paradigm shift is visually represented in Figure 1, highlighting the intricate interplay and collaboration between humans and robots at each workstation.
To optimize the collaborative assignment problem between humans and robots and achieve an efficient production process, it is crucial to develop an assignment strategy that considers the interplay between jobs, robots, and workers.This study introduces a method for job allocation that comprehensively addresses all perspectives, ensuring practical applicability in the production process.The procedure consists of two steps.Initially, tasks are clustered for each collaborative robot to ascertain their assignments.Subsequently, employees are allocated to a set of tasks and collaborative robots.The decision guidelines for planning work among jobs, robots, and workers are categorized into four perspectives, as outlined below.
• Assigning the right robot to the job.(Robot-to-job assignment: R-J) • Selecting the type of job that suits the robot's work limitations.(Job-to-robot assignment: J-R) • Assigning appropriate workers to groups of jobs and robots.
(Worker-to-cobot workstation assignment: W-CW) • Selecting the right group of jobs and robots for workers.

PROPOSED METHOD 2.1 Criteria and Sub-criteria
The criteria employed to assess work and make decisions regarding the assignment of collaborative robots in each of the four perspectives are subject to variation based on the perspective under consideration.To enhance the granularity of assignments, relevant sub-criteria for each criterion are explicitly defined to evaluate resource performance from each perspective.The significance of both the criteria and sub-criteria in evaluating the performance of each perspective is paramount.This is because the data collected for decision-making will be structured according to the relevant sub-criteria of the established criteria.It will then be utilized in determining the most suitable alternative.In the context of this research, post-analysis of data collected according to the specified criteria is essential for the subsequent step of job assignment.Thus, it is evident that the criteria directly impact the job assignment process, ensuring effectiveness, reliability, and the highest degree of accuracy across all four perspectives.Therefore, the criteria set for making decisions on job assignments should comprehensively cover the production line, considering the nuances of each perspective.Further details regarding the sub-criteria linked to each criterion are outlined in Table 1.
Following the identification of criteria (C1-C15) and their associated sub-criteria (S1-S57) for each perspective, the subsequent phase involves data collection to assess the performance of resources (jobs, robots, and workers) based on the established criteria and sub-criteria.This performance data is instrumental in the subsequent assignment of resources.The evaluation of work within each perspective is entrusted to domain experts, individuals with expertise in the respective field.This may include a production line supervisor, experienced workers, and individuals possessing knowledge and understanding of robotics, among others.Their insights and assessments contribute to the informed decision-making process during the assignment of resources in subsequent steps.

Fuzzy Inference System
To analyze the data of factors (or sub-criteria) for each criterion, a Fuzzy Inference System (FIS) [37,38] is utilized.The analysis is carried out independently for all four criteria, using the Mamdani analysis method.The MATLAB program is employed to facilitate calculations.The fundamental structure of a fuzzy inference system consists of four essential components, illustrated in Figure 2.
The details of each element are described as follows [39,40]: • "Fuzzification" process is the creation of a membership function in the form of defining a linguistic variable to be used for converting general or traditional input (crisp input) into input with fuzzy variables (fuzzify input) where the Degree of Membership always has a value in the range between 0-1.
• "Knowledge Base" consists of 2 parts: (1) Rule Base or Fuzzy Rule is the part for defining controls.which is obtained from experts in the form of linguistic rules.( 2) Database is the preparation of necessary parts to be used to define the control and management of fuzzy logic data.• "Inference Engine" plays a pivotal role in the fuzzy inference system, checking facts and rules to interpret reasons.It functions as a mechanism for controlling the utilization of knowledge in problem-solving, akin to determining the approach for reserving valid actions to derive meaningful answers.
• "Defuzzification" process involves transforming data in fuzzy form back to their original values (crisp output), typically ranging between 0 and 1, as initially received from the input.This process includes summarizing the results and making them usable for further applications.Various mathematical methods are employed for defuzzification, with the "Center of Gravity" method being popular in current applications.

Grey Relational Analysis
The Grey Relational Analysis (GRA) [41] technique is employed for the data analysis of each criterion.This is carried out after the analysis of variable data for each criterion using a fuzzy inference system.The equation employed to analyze the grey relationship can be expressed as follows [24,[42][43][44] Equations 1) and ( 2) are used to determine the value of the grey relational generating ( * ) using the analysis "The lower is better" C8 W-CW Efficiency [14,30] C12 Production E nvironments [21] S1 S2 S3 Total cost [30] Cycle time [9,12] Quality [9,30] S14 S15 S16

S13
Cobot proficiency Process speed [12] Executing efficient and safe motions Waiting time [12] S36 S37 S38 S39 Worker availability [30] Training [18] Skill [18,21] Experience  and "The higher is better" respectively, with values in the range [0,1], which the value will be close to 1 when the raw data ( ) considered follows the equation analysis format.Equation 3) is to find the deviation sequence (Δ ) from the reference sequence ( 0 ).By setting the reference sequence equal to 1, the calculated value will be equal to 1 when the data is not consistent with the analysis model.Equations 4)-( 6) are used for finding the grey relational coefficient ( ).In general, the distinguishing coefficient ( ) is usually set to 0.5 [45].Equation 7) is to find the grey relational grade ( ) of each alternative, by considering the importance and weight of each criterion.

The Proposed Two-Step FIS-GRA Integration-Based Multi-Objective Programming Model
The proposed two-step assignment method utilizes a programming model with multiple objectives, specifically Goal Programming [5,24,46].The descriptions of variables used in the lexicographic goal programming model are presented below.Index sets: : Index of robots, = 1, 2, 3, ..., , ℎ: Index of jobs, ℎ = 1, 2, 3, ..., , : Index of cobot workstations, = 1, 2, 3, ..., Ω, : Index of workers, = 1, 2, 3, ..., , : Index of goals, = 1, 2, 3, ..., Decision Variables: ℎ is 1 if a robot is assigned to a jobℎ; otherwise, it is 0, is 1 if a worker is assigned to a cobot workstation ; otherwise, it is 0, ℎ is a positive deviation from the target of the goal for step 1, ℎ is a negative deviation from the target of the goal for step 1, is a positive deviation from the target of the goal for step 2, is a negative deviation from the target of the goal for step 2, * is the optimized negative deviation of the goal , ⊕ is the maximum allowable negative deviation of goal Related Parameter: ℎ is a grey relational grade from ranking a robot for a job ℎ, ℎ is a grey relational grade from ranking a job ℎfor a robot , Ω is a grey relational grade from ranking a worker for a cobot workstation , Ω is a grey relational grade from ranking a cobot workstation for a worker , ℎ is the target of the goal for step1, is the target of the goal for step2, is the maximum number of jobs allowed for the robot 2.4.1 Step 1: FIS-GRA LGP1 model for robot-to-job and job-to-robot assignment.In the initial step of the cobot assignment, the focus on collaborative robots and jobs encompasses two perspectives: the first perspective assigns collaborative robots to jobs, and the second perspective assigns jobs to collaborative robots.The grey relational grade values obtained from both these perspectives will be utilized for job assignments.This implies that in the assignment of one robot to one job, two grey relational grade values are taken into account.These values stem from the analysis of data for each criterion involved in assigning collaborative robots to the job and assigning jobs to collaborative robots, respectively.For the cobot assignment, this research employs the Lexicographic Goal Programming (LGP) method, considering the prioritization of objectives.In the assignment model, two goals are defined, with details outlined in objective functions and constraints.This can be presented as follows: Model LGP1: Subject to: Equation 8) represents the objective function aimed at minimizing negative deviation.Equation 9) represents the primary objective for job assignment in the first perspective, focusing on assigning collaborative robots to jobs.The goal is to identify the highest average grey relational grade.Similarly, Equation 10) serves as the secondary objective for a job assignment in the second aspect, concentrating on a job assignment to collaborative robots, intending to find the highest average grey relational grade.In both objectives, the target value is established at 1, representing the highest achievable average grey relational grade.Given that the average grey relational grade never surpasses 1, it implies that the objective equation will never exceed this value.Consequently, there is no need to consider positive deviation to be subtracted from the target equation.Equation 11) and Equation 12) ascertain the number of collaborative robots to be utilized for a particular job.Conversely, it becomes essential to establish the number of jobs that collaborative robots can manage.Equation 13) necessitates that, in the pursuit of identifying the second optimal solution, the negative deviation of objective 1 should not deteriorate beyond the original level or surpass the negative deviation obtained initially.Additionally, it should potentially not exceed the negative deviation of the first objective that is permitted to be modified.Equation 14) defines the decision variable to possess a binary value of 0 or 1.The ultimate condition stipulates that the negative deviation of both objectives must have a value greater than or equal to 0.
Step 2 involves assigning jobs obtained in Step 1 between workers and cobot workstations.This step includes the third aspect, which assigns workers to the cobot workstation, and the fourth aspect, which assigns cobot workstations to workers.The grey relational grades derived from these two perspectives will be employed for cobot allocation.For cobot assignments, this study utilizes the Lexicographic Goal Programming (LGP) technique, taking into consideration the precedence of objectives.Within the assignment model, we establish two objectives, and their particulars are delineated in the objective function and constraint.This can be articulated in the following manner: Subject to: Equation 20) is the objective function to minimize the negative deviation of two goals.Equation 21) and Equation 22) are the goal conditionals for the third and fourth perspective assignments, respectively.Both conditionals are intended to find the average of the highest grey relational grades.The rationale for excluding positive deviations remains consistent with that in Step 1. Equation 23) and Equation 20) establish the condition for allocating the number of workers to each cobot workstation and, conversely, assigning the number of cobot workstations to each worker.Equations 21)-( 23) mirror the principles outlined in Equations 13)-(15) from Step 1, but Step 2 specifically addresses the relationship between the worker and the cobot workstation.

A CASE STUDY
In this research, a case study of an electronic device assembly line in Thailand was observed.This assembly line includes 3 robots, 3 workers, and 5 types of jobs.Factors or sub-criteria within each criterion were identified to assess the work.The chosen criteria stem from a review of research on cobot assignments, organized based on the 4 perspectives discussed earlier.
After evaluating performance based on factors related to each criterion in each perspective, the next step involves analyzing and evaluating the results of these factors (S) within each criterion (C) using a FIS. Figure 3 provides a visual representation of the calculation of the factor sums for each criterion through the FIS method.The results obtained from the FIS represent the values of each criterion.
The sub-criteria evaluations and FIS outputs for perspectives 1 and 2 are summarized in Table 2, while the results for perspectives 3 and 4 are outlined in Table 3, illustrating the values obtained through the FIS method.These values play a pivotal role in ranking the alternatives through data analysis for each criterion using the GRA method.Once the GRG values for each of the four perspectives are determined, the values obtained from perspectives 1 and 2 are This structured approach ensures a comprehensive consideration of various perspectives in the assignment process.

RESULT AND DISCUSSION
As summarized in Table 4, the results in step 1 of the proposed method revealed that the negative deviation value for assigning robots to jobs was 0.1819.If the negative deviation allowance for the process of assigning robots to jobs is increased by 10%, the negative deviation for assigning robots to jobs rises to 0.1878.Simultaneously, the negative deviation for job assignment to robots decreases from 0.4035 to 0.3032.Similarly, the outcomes in step 2 showed that the negative deviation for assigning workers to a cobot workstation is 0.2636.Allowing a 10% increase in the negative deviation for the process of assigning workers to a cobot workstation to find answers for workers, the negative deviation for worker assignments to the cobot workstation increases to 0.2826.Meanwhile, the negative deviation for cobot workstation assignment to workers decreases from 0.2888 to 0.1821.Moreover, to illustrate the effectiveness of cobot assignments in the collaboration between humans and collaborative robots, alternative methods are presented, and examples of the four considered criteria are thoroughly detailed.Method 1 involves assigning work based on performance, Method 2 utilizes process speed for job assignment, Method 3 relies on random job assignment, and Method 4 is the proposed method.When evaluating productivity, defect safety, and satisfaction, none of the methods yielded better results than the proposed one.However, concerning job switch times, Method 2 outperforms the proposed method by 0.8 minutes per lot.This implies that the jobs assigned by the proposed method may require less job switch time for the robot compared to Method 2, yet it still achieves superior results in terms of productivity, defect safety, and satisfaction.Hence, focusing solely on one perspective doesn't invariably optimize the overall production process.Moreover, it overlooks certain considerations, such as limitations in robot operation and worker safety criteria.The comparative results of all four methods are presented in Table 5.

CONCLUSION
In transitioning from the conventional production model to the era of Industry 5.0, characterized by the concept of collaboration between humans and robots working together, there arises a necessity to develop techniques and methods for addressing problems that may arise in the interaction between human work and collaborative robots.Therefore, this paper introduces a two-step approach for human-robot collaboration assignment: Step 1 involves FIS-GRA LGP1 model for robot-to-job and job-to-robot assignments, and Step 2 entails FIS-GRA LGP2 model for worker-to-robot-job and robotjob-to-worker assignments.The proposed method comprehensively determines assignments for human-robot collaboration by considering four perspectives, striving for optimal overall efficiency.The FIS method is employed to analyze performance sub-criteria in each criterion, and the GRA method ranks alternatives based on criteria values from the FIS analysis.Additionally, LGP is utilized in both assignment steps.This approach allows decision-makers to adjust negative deviation values as necessary to align with their assignment problems.Thus, the proposed method is versatile and efficient for addressing comprehensive human-robot collaboration assignment problems.

Figure 3 :
Figure 3: The sum of factors for each criterion using the FIS method.

Table 1 :
Main criteria and sub-criteria

Table 2 :
Evaluation and Output by FIS for Robot-to-Job Assignment and Job-to-Robot Assignment

Table 3 :
Evaluation and Output by FIS for Worker-to-Cobot Workstation Assignment and Cobot workstation-to-Worker Assignment