Multibody simulation model as part of digital twin architecture: Stewart platform example

Received 5 December 2023, accepted 27 December 2023, date of publication 2 January 2024, date of current version 10 January 2024. Digital Object Identifier 10.1109/ACCESS.2023.3349247 Multibody Simulation Model as Part of Digital Twin Architecture: Stewart Platform Example DOMINIK WALICA AND PETR NOSKIEVIČ Department of Control Systems and Instrumentation, VSB—Technical University of Ostrava, 708 00 Ostrava, Czech Republic Corresponding author: Dominik Walica ([email protected]) This work was supported in part by the European Regional Development Fund in the Research Centre of Advanced Mechatronic Systems Project within the Operational Programme Research, Development, and Education under Grant CZ.02.1.01/0.0/0.0/16_019/0000867; and in part by the Application of Machine and Process Control Advanced Methods through the Ministry of Education, Youth and Sports, Czech Republic, under Project SP2023/074. ABSTRACT The digital twin is considered a new and promising concept whose added value is seen mainly in end applications. However, the benefit of considering the digital twin application since the early development of the system seems not to be stressed enough. The ability to choose system components, methods, and tools can have a symbiotic effect during system integration. This work describes a development process of a Stewart platform digital twin based on its multibody simulation model created in Matlab/Simulink. Although the multibody simulation model is useful in the design phase, after adjustments and verification, it can also be reused as a virtual entity of the digital twin. This integration is enabled by the methods, tools, and system architecture selected for the purpose of including a digital twin. This is considered to be the main contribution of this paper to emerging methodologies for the development of mechatronic systems and its digital twins. However, practical integration comes with challenges that are related to the model fidelity and synchronisation of the virtual and physical entities and are important to overcome in order to employ the system in the real applications. INDEX TERMS Digital twin, machine design, multibody simulation, Stewart platform. I. INTRODUCTION The development of a mechatronic system is a task that requires the involvement of disciplines of mechanical, electrical, and software engineering. The literature describes many mechatronic system development methodologies that begin with the requirements and end with the final product. Many of them are variations of the V-Model. The V-Model describes phases of machine development supported by systems engineering, modelling, and simulation tools. The modelling and simulation tools are used for the analysis and synthesis of the mechatronic system [1],[2]. An example of a mechatronic system is a generally known parallel manipulator, a Stewart platform. In Fig. 1there is a Stewart platform developed and built at VSB - Technical University of Ostrava. It is a parallel robot with six degrees The associate editor coordinating the review of this manuscript and approving it for publication was Mohammad AlShabi . of freedom. It has a wide range of applications in load stabilisation, vibration isolation and generally in areas where spatial motion needs to be simulated in laboratory conditions for testing (e.g. earthquake, flight, driving, or oceanic wave simulation) [3],[4],[5],[6],[7]. However, one of its limitations is the relatively small workspace. Stewart platform generally consists of a base plate, actuators, a moving platform, and upper and lower joints that connect the actuators to the base and the moving platform. When designing a Stewart platform, we are interested in its typical characteristics given by its payload, dynamics, workspace, etc. Some works describe the optimisation of a single aspect of the Stewart platform [8],[9], others focus on the design of a given application [10],[11] or present a general design [12],[13],[14]. To achieve the desired characteristics, we must find the right combination of components that will satisfy our requirements. However, there can also rise nontypical requirements related to the 3700 2024 The Authors. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/ VOLUME 12, 2024 D. Walica, P. Noskievič: Multibody Simulation Model as Part of Digital Twin Architecture FIGURE 1. Stewart platform. current trends of digitalisation that can be taken into account at the beginning of the development process. One of the digitalisation trends is a digital twin. There are many definitions of the digital twin. Nevertheless, recent publications show the opinion seems to be converging to an agreement that the digital twin should consist of a physical entity, virtual entity and a bi-directional connection between them that ensures data/information exchange with the purpose of enhancing the application’s value. The virtual entity can be a representation of the physical entity or its part. Among the characteristics of the digital twin belong its purpose, the level of fidelity of the virtual entity, and the way of data/information exchange [15],[16],[17], [18],[19],[20]. The purpose of the digital twin is often related to fault diagnostics, predictive maintenance, optimisation, etc. Although the concept of digital twin is usually associated with a 3D visualisation, which can provide significant support for decision making, the publications [21],[22] show that it is not a necessary feature. There are many publications that are concerned with the methodology for the development of digital twins [21],[23], [24] or applications [22],[25],[26] related to mechatronic systems. The virtual entity of the digital twin can be physics-based, data-based, or a combination of both [27]. Physics-based models are usually based on simulation models and rely on knowledge of the structure and parameters of the system. Data-based models, on the other hand, often use machine learning methods based on historical and present data. The machine learning model must be trained on the data set that might be provided either by the real measurements, which implies the need for a real system or a physics-based model. Therefore, the combined approach uses physics-based models to train the data-based model [22]. Based on the reviewed literature, the methods and tools used depend on the individual use case. Among the used tools belong software platforms such as Matlab/Simulink, Ansys, Microsoft Azure, etc. [28]. Although the comparison of physics-based and data-based methods is represented in the literature [28] and [29], the comparison of individual software platforms seems to be missing. Carrying out such a study would require access to various software tools and sufficient technical prowess to apply them. There are not many works which concern a digital twin of a Stewart platform or parallel manipulators in general. Huynh et al. [30] present a universal methodology to create serial and parallel manipulator digital twins. The presented methodology shows a uni-directional (one-way) connection from a real robot to the application that reflects its status. It also discusses the possible extension to a bi-directional connection, which would allow responding to anomalies. On the contrary, the works that present serial manipulators are represented more frequently. The work presented by Aivaliotis et al. [21] proposes an approach to enable the implementation of digital twins of industrial robots and complex machines. It also reports on the integration of the approach in a real industrial setting where the digital twin is used for a predictive maintenance application. The methodologies and applications of digital twins are widely represented in the literature. Most of them focus on the development or application of the digital twin concept in an existing system. However, there seems to be a lack of publications that focus on the practical development of the digital twin of the mechatronic system from the early stages of development. Considering the digital twin since the early stages of machine development can bring potential benefits in the system integration stage. On the other hand, it also requires us to take into account considerations that might not be typical in machine development. Therefore, one of the goals of this article is to highlight and discuss these benefits and considerations. This paper presents a development of the Stewart platform digital twin architecture from its early stages. It describes tools and methods that streamline digital twin development. The core of this work are the steps that describe the transformation of the Stewart platform multibody model to the virtual entity of the digital twin. The steps are described to the point where the possibility of bi-directional communication between both entities is presented. This paper does not present the application of the digital twin, but outlines the challenges and benefits of its future implementation. The paper is organised as follows. Section I-A extends this section and introduces the system architecture. Section II presents the design of the kinematic structure of the Stewart platform. Section III describes the creation of the multibody dynamics model for the purpose of machine design. Section IV discusses adjustments of the multibody dynamics model for its verification and shows the results of the multibody dynamics model verification. Section Vshows VOLUME 12, 2024 3701 D. Walica, P. Noskievič: Multibody Simulation Model as Part of Digital Twin Architecture TABLE 1. Stewart platform requirements. the integration of the Stewart platform multibody dynamics model into the digital twin architecture and describes the challenges for the development of digital twin functionalities. Section VI discusses the results, and Section VII summarises the work and proposes future research. A. SYSTEM ARCHITECTURE The design of a system begins with a definition of requirements. In our scenario, the goal was to design a Stewart platform for an experimental mechatronics lab to simulate the spatial motion of a real phenomenon (i.e., vibration). The typical constraints of this scenario are budget and time. A snippet of the general requirements of the Stewart platform itself is shown in Table 1. We decided to not present specific requirement values, as the article is focused more on the digital twin topic than the design of the Stewart platform itself, which has already been documented in the literature. After the initial definition of requirements, it was necessary to make the first design decisions and propose a general system architecture. To have an overview of the requirements and the proposed design, we employed the model-based systems engineering tool System ComposerTM which is Matlab/Simulink’s toolbox, as illustrated in Fig. 2. This tool allows us to link the requirements with the interconnected blocks representing system objects and functions, which should fulfil the requirements. At the beginning of the design phase, the system model can be very general, but becomes more precise with time. Shortly after we get concerned with the type of structure of the Stewart platform, the use of electric or hydraulic actuators, and its control system, we can think about workspace and overload checking functions. At this point, the idea of involving the digital twin for predicting fault states can be included in the solution variants. Therefore, we do not define the digital twin as a requirement, but we define FIGURE 2. The system architecture described in the system composerTM. the required functions of the system that can be fulfilled by employing the digital twin. If we decide to develop this idea, we need to augment our system design with a hardware containing the virtual entity of the digital twin. It also must be decided what kind of model will represent the virtual entity and how the data/information will be exchanged. Multibody simulation in machine design is standard practice in model-based approaches. In our scenario, we could use it not only to verify our design, but also as a virtual entity for the digital twin [31],[32],[33]. From our point of view, the virtual entity could be an augmented simulation model running in parallel to the real machine with an automatic data/information exchange capability and related decisionmaking functions. The verification experiments of the Stewart platform described in the literature used a camera [34], force measurements in the struts [35] or inertial measurement sensors [36], [37]. Camera and inertial measurement sensors are used for an estimation of the kinematic variables. Meanwhile, force measurements are used for the verification of the dynamic properties. Since the authors have experience with modelling and simulation in the Matlab/Simulink environment, the first design variant proposes to create a multibody model with its Simscape Multibody toolbox [38]. Although it should be noted, different options to create a simulation model of the Stewart platform are possible, e.g., using different software for multibody simulation or employing models described in the literature [39],[40], and [41]. A hardware containing the virtual entity in our case could be a real-time target [42], a PC [43], or a machine controller [44]. A necessary condition for the hardware is a sufficient computational power, a communication interface that enables connection to the other devices of the architecture, and the possibility to utilise a Matlab/Simulink model on it. The advantage of using a real-time target is its capability to perform the simulation in real time and its I/O interface. Its disadvantage is the cost and limitation of a fixed-step solver. A PC in contrast can provide a cheaper solution with 3702 VOLUME 12, 2024 D. Walica, P. Noskievič: Multibody Simulation Model as Part of Digital Twin Architecture various options for simulation of a real system. However, at the price of limited real-time simulation capabilities. Employing a machine controller that could also integrate the virtual entity seems to be a perfect solution. The experiment described in [44] and [45] where the simulation of a single hydraulic axis is performed on the PLC (Programmable Logic Controller) for the purpose of virtual commissioning is close to this approach. A design of a machine is an iterative process, and the architecture is refined until the solution variant that meets all the requirements is found. The selection and design process of most system components is not described in this article, since it would exceed its scope. The resulting choices are captured in the designed digital twin architecture shown in Fig. 3. The methods and tools for developing the physical and virtual entity of the Stewart platform digital twin are described in the following sections. The Stewart platform as a physical entity is controlled via a Bosch MLC XM21 machine controller that allows synchronised motion control of six Bosch EMC-063 linear electric actuators through Bosch HCS01 compact converters and the SERCOS communication interface. An important tool that the controller offers is its Open Core Interface (OCE). The OCE allows the user to control the linear electric actuators through the Matlab and Simulink environment [46], [47]. This is beneficial for the integration of the multibody model as a virtual entity, as shown in Section V. A PC performed well in solving the Stewart platform multibody model, as shown in Section IV. Therefore, we decided to use it as both a platform for a virtual entity and an operator workstation with a Matlab-based user control interface. The PC configuration includes CPU Intel(R) Core(TM) i5-13600K at 3.5 GHz, GPU NVIDIA GeForce RTX 3080 Ti, 32 GB RAM, and Windows 10 Pro 64-bit. For the purpose of the verification experiment and the development of digital twin-based functions, Comforia MCF150-5kN load cells for force measurement have been included in the design. The load cells are connected to the amplifiers that adjust the measured signals to the ±10 V range suitable for the analog inputs of the dSPACE MicroLabBox measurement unit. The signals are processed, and the resulting data are sent over the local area network (LAN) to the PC. The central node of the LAN is a router that connects the other devices to the star topology. II. STEWART PLATFORM—KINEMATIC STRUCTURE A design of the mechanical part of the Stewart platform starts with its kinematic structure. In our case, we decided to select the structure with linear actuators that are represented as struts as indicated in Fig. 4. The pose of the Stewart platform is determined by the position and orientation of its moving plate. The position and orientation depend on the length of the struts and joint positions of both plates. The leg vector li is determined by the inverse kinematics (1) and consequently the length of the strut is given by (2). li=r+Rap i−bi(1) |li| = pli·li i=1,2,...,6 (2) where ris a position vector of the reference frame of the moving plate with respect to the reference frame of the base plate, Ris the rotation matrix, ap iis the vector related to the reference frame of the moving plate representing the joint position of the moving plate, similarly biis the vector related to the reference frame of the base plate representing the joint position of the base plate. As depicted in Fig. 5the points Biand Pirepresent the joint coordinates of the base plate and the moving plate, respectively. The designer specifies the radiuses rband rp, and the offset angles βand α. Without offset angles, the symmetry axes of each respective plate are shifted by 120◦. The offset between the symmetry axes of the base and the moving plate is 60◦. The initial configuration of the Stewart platform is determined by the minimal length of the linear actuator and joint positions. The specification of the minimum leg length lmin allows us to calculate the minimum height of the Stewart platform Zmin by (3). Zmin =ql2 min −(Pxi−Bxi)2−(Pyi−Byi)2(3) where Pxi,Bxi,Pyi, and Byiare the coordinates xand yof the moving and base plate joints. Leg length lmin is the distance between the pair of joints in the default position of the Stewart platform. This implies that an arbitrary platform and base joint pair (Bi,Pi) can be selected for the calculation. The length of the strut is limited by its minimum and maximum length, as given by (4). Where lextension is the maximum leg extension. lmin ≤ |li| ≤ lmax lmax =lmin +lextension (4) Another constraint is imposed by the joint angles between the leg, the moving platform, and the base plate. The joint angle between the leg and the moving plate can be calculated according to (5). γi=arccos( li·v |li||v|) (5) where γiis the angle between the leg vector liand the vector v that is perpendicular to the moving plate. Equation (5) can be applied to calculate the angle between the leg vector and the static base plate if we substitute vwith nwhich represents the normal vector to the base plate. This angle will be represented by ηi. The constraints of the joint angles γiand ηiare given by (6). |γi| ≤ γmax,|ηi| ≤ ηmax (6) To obtain a larger workspace, it is often beneficial to align the joint axis with the leg vector liin the default position of VOLUME 12, 2024 3703 D. Walica, P. Noskievič: Multibody Simulation Model as Part of Digital Twin Architecture FIGURE 3. The designed Stewart platform digital twin architecture. FIGURE 4. General kinematic structure of the Stewart platform. the Stewart platform. The lower joint axis is jbi. As a result, we will get zero initial joint angles. For the base joint angle ηithe (5) is slightly modified to (7) [48]. ηi=arccos( li·jbi |li||jbi|) (7) To calculate the angle γibetween the leg vector liand the upper joint axis is jpiwe must rotate jpiwith the moving plate as shown in (8). γi=arccos(li·(−Rjpi) |li||jpi|) (8) FIGURE 5. Stewart platform base and moving plate joint positions. A. STEWART PLATFORM DESIGN APPLICATION The kinematic structure of the Stewart platform was synthesised and analysed in an iterative manner using an application created in Matlab App Designer shown in Fig. 6. Among the main features of the application belong the parameterisation of the kinematic structure, investigation of the workspace, and export of the structure parameters to the file. The application also allows saving current and loading past kinematic structure parameters. The application is based on the equations presented earlier in this section. On the left side of Fig. 6is a control panel with input fields and buttons that allows the user to parameterise 3704 VOLUME 12, 2024 D. Walica, P. Noskievič: Multibody Simulation Model as Part of Digital Twin Architecture the general kinematic structure of the Stewart platform by specifying the base and platform radiuses rband rp, the offset angles βand α, the maximum actuator extension lextension and the minimum length of the strut lmin which is given by the length of the actuator body with a fully retracted piston. By entering these parameters, the application can calculate the minimum height Zmin of the Stewart platform. Based on the input parameters provided, the Stewart platform configuration can be plotted in an arbitrary position and orientation, as shown on the upper right side of Fig. 6. Below the graph are the values of actual leg lengths |li|and joint angles γiand ηi. The joint angles can be evaluated with respect to either the joint axis perpendicular to the plate or the joint axis aligned with the leg in the default position, as was explained earlier. By this means, we can explore either a single position and orientation or a predefined set. A predefined set is a variable that contains workspace points that are to be investigated. These are the red points on the plot on the upper right side of Fig. 6. Although this allows us to evaluate different configurations, we cannot estimate the mechanism workspace without defining constraints. To perform a workspace analysis, we need to select constraints lmin,lmax,γmax, and ηmax. Here lmax is given by the sum of the actuator body length and its maximum extension. In our case, we determined the constraints from the parameters of the strut configuration. The strut configuration consists of a lower and upper joint, a linear actuator, a load cell, and mounting parts. Parameters were taken from the datasheets of the preselected equipment. The selection of the linear actuator and load cell was based on the payload and required dynamic properties. The joint positions Band Pwere determined on the basis of the analysis of the workspace. Workspace analysis is performed by determining the constant-orientation workspaces of the Stewart platform. This is accomplished by evaluating a set of desired workspace positions with constant-orientation of the Stewart platform. If the constraints are not violated, the point belongs to the constant-orientation workspace, as shown in Fig. 7. It helped us find constant-orientation workspaces for boundary values and decide if it is viable to proceed with the configuration. In the application, we do not check for body collisions and singularities. Body collisions are checked with both basic calculations based on the shape of the selected linear actuator and visually in the CAD software. Due to the selected configuration of the Stewart platform, we assume that the singularities are not within the specified workspace. After the initial analysis, the data files describing the kinematic configuration are exported and used in Autodesk Inventor CAD software. The output files contain the joint coordinates Band Pof the base and moving plate, the body length of the actuator lmin and the maximum extension of the actuator lextension to parameterize the 3D models of the base and moving plate, and linear actuators that are combined in the assembly model of the Stewart platform. Based on joint alignment, it can also contain data describing the upper and lower joint axis vectors jpiand jbithat are crucial for the configuration of a proper joint orientation. A sketch of the joint positions of the base plate is shown in Fig. 8. The dimensions of the sketch are parameterized by the base joint coordinates B. In case the output data files are changed, the sketch is updated, and therefore the whole assembly. By this approach, we could evaluate multiple variants relatively quickly. After assigning realistic physical properties to the bodies or its direct replacement by CAD models of its real counterparts, the selected variant is transformed into the multibody simulation model for further analysis. The presented method can also be extended for parameterisation of the multibody simulation model [49]. III. STEWART PLATFORM—CREATING A MULTIBODY DYNAMICS MODEL Unfortunately, the kinematic structure will not help us evaluate the dynamics requirements on the Stewart platform. The dynamics of the Stewart platform will be mainly determined by the choice of actuators and its control system. However, the dimensions of the selected equipment must either fit our kinematic structure or be adjusted. To support the development process, it is essential to employ tools for modelling and simulation. As described in Section II-A we first chose the linear actuators and built the structure around them (Fig. 9). The presented solution variant meets the requirements described in Table 1that concern the mechanical design. Assembly parts are either commercially available (e.g., linear actuators, load cells, spherical joints, etc.) or manufactured (e.g., base and moving plate, etc.). The manufactured parts are based on the drawings generated from the CAD model. Linear actuators have been selected on the basis of experiments with multiple iterations of a multibody model. The problem with the multibody model is that we cannot verify it until the real machine is built. In our case, the motivation to build and verify a multibody model stems both from the design and from the perspective of the digital twin application. The CAD model in Fig. 9describes the real Stewart platform shown in Fig. 1. However, generating a multibody model directly from this configuration would lead to a complex and computationally demanding model. The CAD model consists of parts (e.g., bolts, wheels, mounting equipment, etc.) that are essential for the function of the real Stewart platform but unimportant for the multibody simulation model. Another issue represent parts that form a functional unit but are interconnected by fixed constraints, e.g., piston parts, linear actuator mechanical drive and electrical motor, etc. The number of bodies and joints increases the complexity of the model. Therefore, to obtain the best possible performance, it is necessary to reduce the number of these elements to the minimum. The mass of the removed parts is added to the relevant bodies. The remaining bodies are considered homogeneous. VOLUME 12, 2024 3705 D. Walica, P. Noskievič: Multibody Simulation Model as Part of Digital Twin Architecture FIGURE 6. Stewart platform design application. After the preparation of the CAD model, the next step is the generation of the multibody model with the use of the Simscape Multibody Link plug-in. It generates the XML multibody description file and a set of body geometry files. The files are then imported to Matlab and based on them a reduced multibody simulation model of the Stewart platform is generated. The structure of the multibody model must be checked to ensure that it was generated correctly. To verify this, Matlab/Simulink offers diagnostic tools that report some of the model problems. The multibody simulation model can also be visually inspected (Fig. 10) to see whether it resembles the modelled system. The visualisation tool is also viable during the digital twin experiments presented in Section V-B. After setting up a gravity vector and constraints, it can be checked if the model does not fall apart by the effect of the gravitational force or violated constraints. Some of the parameters, such as joint limits, must be set as well, since they may not be transferred directly from the CAD software. The joints that represent linear actuators must be set in a forward or inverse dynamics regime to analyse motion profiles and acting forces. The refined multibody simulation model is the main part of a block diagram in Fig. 11. The measurement block encompasses all scopes for tracking values related to the Stewart platform. It ranges from leg extensions, moving plate position and orientation to the joint angles and forces exerted by the linear actuators. The trajectory generator block shown in Fig. 11 serves to plan a trajectory of the moving plate. The inverse kinematics block transforms the trajectory point into the required leg lengths. The output signals that carry the leg length values lead to the blocks that convert the Simulink signal into the Simscape physical signal. This block also functions as a second-order low-pass filter that can provide the first and 3706 VOLUME 12, 2024 D. Walica, P. Noskievič: Multibody Simulation Model as Part of Digital Twin Architecture FIGURE 7. Workspace analysis for the constant-orientation (10◦, 0◦, 0◦) workspace of the Stewart platform. FIGURE 8. Parameterized joint positions of the base plate. second derivatives of the input. The converted signals lead to cylindrical joint blocks set into the inverse dynamics regime. The cylindrical joint represents a linear actuator that consists of its body and an extensible piston. The extensible piston changes the length of the strut. At this phase, the multibody model allows us to test arbitrary motion profiles of the moving plate (Fig. 12) and determine if the piston extensions (Fig. 13), velocities (Fig. 14), accelerations and forces (Fig. 15) are in the limits given by the linear actuator manufacturer. IV. STEWART PLATFORM—MULTIBODY DYNAMICS MODEL VERIFICATION As foreshadowed earlier, since we plan to employ the multibody model as a virtual entity, we need to verify it. To verify the multibody model, we must compare relevant machine states with its simulated counterparts. In our case, the model is verified based on the force measurements FIGURE 9. Stewart platform CAD model. FIGURE 10. Multibody model of the Stewart platform. obtained from the load cells whose location can be seen in Fig. 9. In the previous Section III we have reduced the linear actuator to two parts, the body and the piston. Since the piston is reduced to the single body, we cannot obtain the force acting on the load cell but only the force exerted through the cylindrical joint (Fig. 16(a)). In practice, it is possible to obtain the acting force of a linear actuator by measuring the motor currents and knowing the relevant parameters of the motor and linear drive. However, these parameters can be difficult or even impossible to obtain. The accuracy of such an approach can also be insufficient. Therefore, the reason the load cell is included in our design is better measurement accuracy. The used load cells can measure forces in both push and pull directions up VOLUME 12, 2024 3707 D. Walica, P. Noskievič: Multibody Simulation Model as Part of Digital Twin Architecture FIGURE 11. Stewart platform multibody Simulink diagram. FIGURE 12. Stewart platform motion profile. TABLE 2. Maximum error of Comforia MCF150-5kN load cell. to the 5 kN range. Its maximum error given by a manufacturer is shown in Table 2. The single-body piston model variant was sufficient for machine design. However, for the purpose of model verification, we developed a second version of the model. In the second version, we divide the piston into two bodies. The piston is split in the position of the load cell. The acting force is measured with respect to its reference frame shown FIGURE 13. Piston extensions. FIGURE 14. Piston velocities. in Fig. 16(b). The two piston bodies are connected by a fixed constraint (Weld joint). This modification will add six more bodies to the system, and therefore it increases the computational load in exchange 3708 VOLUME 12, 2024 D. Walica, P. Noskievič: Multibody Simulation Model as Part of Digital Twin Architecture However, this integration also presents challenges given by model fidelity, related measurement errors, and the synchronisation of virtual and physical entities (i.e., communication delay, measurement distortion). These properties can directly affect the overload and workspace check functions. This implies that the virtual entity must be up to date representation of the real entity, otherwise the measurements will differ significantly from its virtual counterparts, which will result in digital twin not fulfilling its purpose properly. In other words, it can result in false detection of a critical condition, non-detection of a critical condition, or late response to a critical condition. Although we presented possible solutions for these challenges, it is evident that using the presented digital twin concept in a real application requires increasing the robustness of the system. The first step towards this would be to include a dedicated hardware platform for the virtual entity (e.g., real-time target as mentioned in I-A) or include the virtual entity into the machine controller which currently seems to be more futuristic variant. It could also be argued that the prediction of exceeding maximum forces and joint angles could be performed offline solely with known inputs and a simulation model that would be periodically updated. Especially if we consider the issues with the synchronisation of virtual and physical entities. However, this configuration would disable a valuable feature, the online evaluation of the difference between measured and calculated force. The difference between measured and calculated force can indicate the change in model parameters (change of load, mechanical faults, etc.) but also collisions with objects. Exceeding the force difference can result in issuing a command to stop the machine. The Stewart platform fault prediction concept as presented in this paper can be useful in applications where the trajectory is known in advance (e.g., life cycle testing). On the other hand, in use cases where the trajectory is not known beforehand (e.g., vehicle simulators), it is not viable. In such cases, only actual and past states could be compared, which can still be valuable, as explained in the previous paragraph. However, the virtual entity would have to be modified to receive online inputs and issue motion commands throughout the simulation, not only at the beginning. VII. CONCLUSION In this paper, a development process of the Stewart platform digital twin is presented from its early stages. The idea of employing a digital twin is shown to originate from the requirements of the system. Based on the requirements, suitable tools and methods that consider the digital twin as well as the system architecture are selected and briefly explained. The next step, which is concerned with the kinematic structure of the Stewart platform, does not really differ from the typical development process. However, it cannot be omitted since it is a preliminary step in the creation of the multibody model of the Stewart platform. In Sections III and IV we present that in this phase we must take into account both the model fidelity and the computational complexity of the multibody dynamics model. This is for the sake of its subsequent use as a virtual entity of the digital twin. To use the multibody model in the model verification experiment, we created a model variant with a piston divided into two bodies. In the verification experiment, we compared measured and calculated forces with the use of cross-covariance. This was enabled by introducing load cells into the system architecture. The results of the verification were sufficient. Although it has been stated that differences between the signals can be caused by multiple factors ranging from making too many simplifications to the imprecise transformation of the blueprints to the reality. Additionally, the measurement error also represents an intervening factor. In combination with computational limitations, these are the reasons why achieving a perfect digital representation of the real object is very difficult or almost unattainable. Therefore, uncertainty must be taken into account. The last section describes the integration of the multibody model as a virtual entity of the digital twin that runs ahead in parallel to the physical entity. It presents the capability of the bi-directional communication between both real and virtual entities and basic overload and workspace check functions. Through the virtual entity, we can evaluate measured and simulated forces of the real machine and also issue commands to the control system of the Stewart platform as described in the presented experiment results. This experiment revealed some of the challenges given by model fidelity, related measurement errors, and the synchronisation of virtual and physical entities (i.e., communication delay, measurement distortion) that need to be addressed in future work. The main contribution to the development of the digital twin technology presented in this work is the idea of aligning tools and methods that allow reuse of the developed multibodysimulationmodelanditsintegrationintothedigital twin architecture. This is demonstrated on the example of the Stewart platform with the intended use of a digital twin for fault prediction applications. This work lays the foundation for the next series of experiments that will focus on the robustness and implementation of the digital twins based on multibody simulation models in real applications. This can include evaluating different approaches and software platforms to develop the multibody dynamics-based virtual entity of a digital twin. REFERENCES [1] I. Graessler, J. Hentze, and T. Bruckmann, ‘‘V-models for interdisciplinary systems engineering,’’ in Proc. Design 15th Int. Design Conf., 2018, pp. 747–756. [2] G. Barbieri, C. Fantuzzi, and R. Borsari, ‘‘A model-based design methodology for the development of mechatronic systems,’’ Mechatronics, vol. 24, no. 7, pp. 833–843, Oct. 2014. [3] X. Liu and R. D. Wiersma, ‘‘Optimization based trajectory planning for real-time 6DoF robotic patient motion compensation systems,’’ PLoS ONE, vol. 14, no. 1, Jan. 2019, Art. no. e0210385. VOLUME 12, 2024 3715 D. Walica, P. Noskievič: Multibody Simulation Model as Part of Digital Twin Architecture [4] A. Preumont, M. Horodinca, I. Romanescu, B. de Marneffe, M. Avraam, A. Deraemaeker, F. Bossens, and A. Abu Hanieh, ‘‘A six-axis singlestage active vibration isolator based on stewart platform,’’ J. Sound Vibrat., vol. 300, nos. 3–5, pp. 644–661, Mar. 2007. [5] C. Du, T. Wang, H. Zhou, Z. Sun, and Y. Lei, ‘‘Development of an integrated load testing device for a substructure hybrid test of a curved bridge,’’ Experim. Techn., vol. 46, no. 3, pp. 395–411, Jun. 2022. [6] V. S. Arconada, J. García-Barruetabeña, and R. Haas, ‘‘Validation of a ride comfort simulation strategy on an electric stewart platform for real road driving applications,’’ J. Low Freq. Noise, Vibrat. Act. Control, vol. 42, no. 1, pp. 368–391, Mar. 2023. [7] D. Silva, J. Garrido, and E. Riveiro, ‘‘Stewart platform motion control automation with industrial resources to perform cycloidal and oceanic wave trajectories,’’ Machines, vol. 10, no. 8, p. 711, Aug. 2022. [8] M. Toz and S. Kucuk, ‘‘Dexterous workspace optimization of an asymmetric six-degree of freedom Stewart–Gough platform type manipulator,’’ Robot. Auto. Syst., vol. 61, no. 12, pp. 1516–1528, Dec. 2013. [9] H. Tourajizadeh, M. Yousefzadeh, and A. Tajik, ‘‘Closed loop optimal control of a stewart platform using an optimal feedback linearization method,’’ Int. J. Adv. Robotic Syst., vol. 13, no. 3, p. 134, May 2016. [10] H. Yun, L. Liu, Q. Li, W. Li, and L. Tang, ‘‘Development of an isotropic Stewart platform for telescope secondary mirror,’’ Mech. Syst. Signal Process., vol. 127, pp. 328–344, Jul. 2019. [11] X. Song, Y. Pan, and Y. Chen, ‘‘Development of a low-cost parallel kinematic machine for multidirectional additive manufacturing,’’ J. Manuf. Sci. Eng., vol. 137, no. 2, Apr. 2015, Art. no. 021005. [12] M. Hiller, S. Fang, S. Mielczarek, R. Verhoeven, and D. Franitza, ‘‘Design, analysis and realization of tendon-based parallel manipulators,’’ Mechanism Mach. Theory, vol. 40, no. 4, pp. 429–445, Apr. 2005. [13] T.-L. Wu, J.-H. Chen, and S.-H. Chang, ‘‘A six-DOF prismatic-sphericalspherical parallel compliant nanopositioner,’’ IEEE Trans. Ultrason., Ferroelectr., Freq. Control, vol. 55, no. 12, pp. 2544–2551, Dec. 2008. [14] H. C. G. Pritschow and K.-H. Wurst, ‘‘Systematic design of hexapods and other parallel link systems,’’ CIRP Ann., vol. 46, no. 1, pp. 291–295, 1997. [15] M. Grieves and J. Vickers, ‘‘Digital twin: Mitigating unpredictable, undesirable emergent behavior in complex systems,’’ in Transdisciplinary Perspectives on Complex Systems: New Findings and Approaches. Cham, Switzerland: Springer, 2016, pp. 85–113. [16] A. Fuller, Z. Fan, C. Day, and C. Barlow, ‘‘Digital twin: Enabling technologies, challenges and open research,’’ IEEE Access, vol. 8, pp. 108952–108971, 2020. [17] Y. K. Liu, S. K. Ong, and A. Y. C. Nee, ‘‘State-of-the-art survey on digital twin implementations,’’ Adv. Manuf., vol. 10, no. 1, pp. 1–23, Jan. 2022. [18] J.-F. Yao, Y. Yang, X.-C. Wang, and X.-P. Zhang, ‘‘Systematic review of digital twin technology and applications,’’ Vis. Comput. Ind., Biomed., Art, vol. 6, no. 1, p. 10, May 2023. [19] E. VanDerHorn and S. Mahadevan, ‘‘Digital twin: Generalization, characterization and implementation,’’ Decis. Support Syst., vol. 145, Jun. 2021, Art. no. 113524. [20] D. Jones, C. Snider, A. Nassehi, J. Yon, and B. Hicks, ‘‘Characterising the digital twin: A systematic literature review,’’ CIRP J. Manuf. Sci. Technol., vol. 29, pp. 36–52, May 2020. [21] P. Aivaliotis, Z. Arkouli, K. Georgoulias, and S. Makris, ‘‘Methodology for enabling dynamic digital twins and virtual model evolution in industrial robotics—A predictive maintenance application,’’ Int. J. Comput. Integr. Manuf., vol. 36, no. 7, pp. 947–965, Jul. 2023. [22] L. Wang, Y. Liu, H. Yin, and W. Sun, ‘‘Fault diagnosis and predictive maintenance for hydraulic system based on digital twin model,’’ AIP Adv., vol. 12, no. 6, Jun. 2022, Art. no. 065213. [23] X. Zhang, B. Wu, X. Zhang, J. Duan, C. Wan, and Y. Hu, ‘‘An effective MBSE approach for constructing industrial robot digital twin system,’’ Robot. Comput.-Integr. Manuf., vol. 80, Apr. 2023, Art. no. 102455. [24] Y. Wei, T. Hu, P. Yue, W. Luo, and S. Ma, ‘‘Study on the construction theory of digital twin mechanism model for mechatronics equipment,’’ Int. J. Adv. Manuf. Technol., pp. 1–19, Apr. 2022. [25] M. Matulis and C. Harvey, ‘‘A robot arm digital twin utilising reinforcement learning,’’ Comput. Graph., vol. 95, pp. 106–114, Apr. 2021. [26] K. Classens, W. P. M. H. M. Heemels, and T. Oomen, ‘‘Digital twins in mechatronics: From model-based control to predictive maintenance,’’ in Proc. IEEE 1st Int. Conf. Digit. Twins Parallel Intell. (DTPI), Jul. 2021, pp. 336–339. [27] D. Adamenko, S. Kunnen, R. Pluhnau, A. Loibl, and A. Nagarajah, ‘‘Review and comparison of the methods of designing the digital twin,’’ Proc. CIRP, vol. 91, pp. 27–32, Jan. 2020. [28] M. Ibrahim, V. Rjabtšikov, and R. Gilbert, ‘‘Overview of digital twin platforms for EV applications,’’ Sensors, vol. 23, no. 3, p. 1414, Jan. 2023. [29] A. Regis, S. Arroyave-Tobon, J.-M. Linares, and E. Mermoz, ‘‘Physicbased vs data-based digital twins for bush bearing wear diagnostic,’’ Wear, vols. 526–527, Aug. 2023, Art. no. 204888. [30] B. H. Huynh, H. Akhtar, and M. K. Sett, ‘‘A universal methodology to create digital twins for serial and parallel manipulators,’’ in Proc. IEEE Int. Conf. Syst., Man Cybern. (SMC), Oct. 2019, pp. 3104–3109. [31] E. Kurvinen, ‘‘Physics-based digital twins merging with machines: Cases of mobile log crane and rotating machine,’’ IEEE Access, vol. 10, pp. 45962–45978, 2022. [32] Q. Khadim, Y. S. Hagh, L. Pyrhönen, S. Jaiswal, V. Zhidchenko, E. Kurvinen, J. Sopanen, A. Mikkola, and H. Handroos, ‘‘State estimation in a hydraulically actuated log crane using unscented Kalman filter,’’ IEEE Access, vol. 10, pp. 62863–62878, 2022. [33] V. Zhidchenko, I. Malysheva, H. Handroos, and A. Kovartsev, ‘‘Faster than real-time simulation of mobile crane dynamics using digital twin concept,’’ J. Phys., Conf. Ser., vol. 1096, Sep. 2018, Art. no. 012071. [34] C. Schempp and S. Schulz, ‘‘High-precision absolute pose sensing for parallel mechanisms,’’ Sensors, vol. 22, no. 5, p. 1995, Mar. 2022. [35] Z.-F. Shao, X. Tang, and L. Wang, ‘‘Dynamics verification experiment of the Stewart parallel manipulator,’’ Int. J. Adv. Robotic Syst., vol. 12, no. 10, p. 144, Oct. 2015. [36] S. A. Maged, A. A. Abouelsoud, A. M. R. F. E. Bab, and T. Namerikawa, ‘‘Stewart platform manipulator: State estimation using inertia sensors and unscented Kalman filter,’’ in Proc. 3rd Int. Conf. Inf. Sci. Control Eng. (ICISCE), Jul. 2016, pp. 1136–1140. [37] I. Miletović, D. M. Pool, O. Stroosma, M. M. van Paassen, and Q. P. Chu, ‘‘Improved Stewart platform state estimation using inertial and actuator position measurements,’’ Control Eng. Pract., vol. 62, pp. 102–115, May 2017. [38] P. Noskievic and D. Walica, ‘‘Design and realisation of the simulation model of the Stewart platform using the MATLAB-simulink and the simscape multibody library,’’ in Proc. 21st Int. Carpathian Control Conf. (ICCC), Oct. 2020, pp. 1–5. [39] H. Hajimirzaalian, H. Moosavi, and M. Massah, ‘‘Dynamics analysis and simulation of parallel robot stewart platform,’’ in Proc. 2nd Int. Conf. Comput. Autom. Eng. (ICCAE), vol. 5, Feb. 2010, pp. 472–477. [40] W. Zhu, M. Jiang, F. Yang, and X. Rui, ‘‘Modeling of a hexapod piezoactuated positioning platform,’’ Multibody Syst. Dyn., pp. 1–24, Jun. 2023. [41] G. Kazezkhan, B. Xiang, N. Wang, and A. Yusup, ‘‘Dynamic modeling of the Stewart platform for the NanShan radio telescope,’’ Adv. Mech. Eng., vol. 12, no. 7, Jul. 2020, Art. no. 168781402094007. [42] F. Toso, R. Torchio, A. Favato, P. G. Carlet, S. Bolognani, and P. Alotto, ‘‘Digital twins as electric motor soft-sensors in the automotive industry,’’ in Proc. IEEE Int. Workshop Metrol. Automot. (MetroAutomotive), Jul. 2021, pp. 13–18. [43] C.-J. Liang, W. McGee, C. C. Menassa, and V. R. Kamat, ‘‘Real-time state synchronization between physical construction robots and process-level digital twins,’’ Construct. Robot., vol. 6, no. 1, pp. 57–73, Mar. 2022. [44] N. Menager, N. Worschech, and L. Mikelsons, ‘‘A toolchain for rapid control prototyping using rexroth controllers and open source software,’’ in Proc. Linköping Electron. Conf., Mar. 2014, pp. 371–380. [45] N. Menager, R. Kampfmann, N. Worschech, and L. Mikelsons, ‘‘Suitability of different real-time solvers for a model-based engineering toolchain using industrial rexroth controllers,’’ in Proc. Linköping Electron. Conf. Proc., Sep. 2015, pp. 883–891. [46] MathWorks. Open Core Interface SDK for MATLAB and Simulink. Natick, MA, USA. Accessed: Dec. 30, 2023. [Online]. Available: https://www.mathworks.com/products/connections/product_detail/opencore-interface.html. [47] Bosch Rexroth AG. MATLAB Reference (MLPI4MATLAB). Lohr am Main, Germany. Accessed: Dec. 30, 2023. [Online]. Available: https://apps.boschrexroth.com/docs/oci/mlpi4matlab/ [48] I. A. Bonev and J. Ryu, ‘‘A new approach to orientation workspace analysis of 6-DOF parallel manipulators,’’ Mechanism Mach. Theory, vol. 36, no. 1, pp. 15–28, Jan. 2001. 3716 VOLUME 12, 2024 D. Walica, P. Noskievič: Multibody Simulation Model as Part of Digital Twin Architecture [49] M. Mohammadi, E. Kurvinen, and A. Mikkola, ‘‘A design process to parameterize a real-time simulation model of a commercial vehicle,’’ Int. Rev. Mech. Eng. (IREME), vol. 13, no. 12, p. 673, Dec. 2019. [50] J. Czebe, P. Šuránek, J. Tuma, and D. Fojtík, ‘‘Finding similarities in laser micrometers scanned data using cross-covariance,’’ in Proc. 20th Int. Carpathian Control Conf. (ICCC), May 2019, pp. 1–4. [51] H. Palahalli, E. Ragaini, and G. Gruosso, ‘‘Real-time smart microgrid simulation: The integration of communication layer in electrical simulation,’’ in Proc. 22nd IEEE Int. Conf. Ind. Technol. (ICIT), vol. 1, Mar. 2021, pp. 631–636. [52] R. Eskola, H. Korpilahti, B. Bozorgmehri, M. K. Matikainen, and A. Mikkola, ‘‘Real-time multi-body co-simulation model of a veneer peeling lathe,’’ Int. J. Comput. Integr. Manuf., vol. 36, no. 4, pp. 634–656, Apr. 2023. [53] Y. Zan, D. Han, L. Yuan, M. Liu, and Z. Wu, ‘‘Research on real-time simulation system of ship motion based on simulink,’’ Open Mech. Eng. J., vol. 8, no. 1, pp. 820–827, Dec. 2014. DOMINIK WALICA received the M.Sc. degree in automatic control and engineering informatics from the VŠB—Technical University of Ostrava (VŠB-TUO), Czech Republic, in 2019. Since 2019, he has been a Junior Researcher with the Department of Control Systems and Instrumentation, Faculty of Mechanical Engineering, VŠB-TUO. His research interests include modelling and simulation of mechatronic systems, Stewart platform, and digital twin. PETR NOSKIEVIČ was born in Ostrava, Czech Republic, in 1959. He received the Doctor (Associate Professor) degree, in 1992. After dissertation the VŠB-Technical University of Ostrava (VŠB-TUO), he worked for eight years in the industry in control of hydraulic drives, in 1987, where he has been an Associate Professor with the Faculty of Mechanical Engineering, since 1994. In 2001, he was a Full Professor in control of machines and processes and continued with VŠBTUO. He delivers lectures from modelling and simulation of mechatronic systems, system identification, and control of fluid power actuators. He introduced the bachelor’s and master’s study programme mechatronics with VŠBTUO. He is a supervisor and a guarantor of the Ph.D. Study Programme Control of Machines and Processes with the Faculty of Mechanical Engineering. His main research interests include modelling, simulation, and control of hydraulic drives. He was the Chairperson of the Organization Committee of the Czech Association for Hydraulics and Pneumatics, from 2001 to 2023, and a member of the REM Network for Research and Education in Mechatronics and Fluid Power Net International—FPNI, from 2003 to 2018 and from 2000 to 2014. VOLUME 12, 2024 3717