Part Of Robot Research Articles

Design and Testing of Brush Robot as Innovation in Improving STEM Instructional Out-Come in Pre-Service Teachers in Plateau State.

In this study, an experimental research design was used to design and test brush robots with pre-service teachers in Federal College of Education Pankshin Plateau state. This intends to solve the problem of innovation deficit in classroom instruction. The population for the study consisted of all NCE one students in the department of early childhood offering the course Science Technology Engineering and Mathematics STEM in the 2023/2024 session. A Sample of 30 Pre service NCE teachers participated in the research. A robot brush was constructed using low cost kits in the robot design stages. The instruments used consisted of Robot Parts test and the Solve-It tasks (design and functionality test) with Cronbach alpha reliability of 0.81. Treatment lasted for 6 weeks. Data was collected and analysed using descriptive and inferential statistics. Results indicated that pre-service teachers have poor knowledge of robot parts such as DC motors. This implies that pre-service teachers are novice to robot part and use Also, participants were very competent in robot design process activities and robot base cutting. Participants also showed average competence in Robot stage cutting, construction of rollers and fixing of robot parts. They however showed only fair competence in coupling of robots parts. Findings indicate that the teachers designed robots have high educational value. The robots are averagely complete in form, ease of use motion and durability. The designs however have low compliance to safety. It was recommended amongst other that Teacher training colleges should organised in-service training to improve teacher competent in handling engineering and technology parts and programming of STEM robots.

Initial experience with a 5G cellular network and robotic arm-based remote echocardiographic system in an all-comers setting

Abstract Background Echocardiography is the test-of-choice for the initial evaluation of many cardiac diseases and requires expertise that is often limited in rural area. Robotic arm-assisted remote echocardigram has been attampted for teleconsultation but was limited to heart failure patients(ref), primarily due to the network delay in telecommunication and the subsequent incoordination in robotic arm control. Purpose We aim to assess the feasibility and diagnostic accuracy of a 5G cellular network and robotic arm-based remote echocardiographic system in an all-comers setting. Methods 51 pts were enrolled from the outpatient cardiology clinic of our institute. All pts underwent standard comprehensive echocardiography on a 5G cellular network and robotic arm-based remote echocardiographic system (the robotic part was deployed at our hospital and the control part was located at another campus 20 kilometers away) (Figure 1)and a conventional echocardiographic platform (at our hospital) successively. The order in which patients were examined on the remote and conventional instruments was randomly determined. There was no interval between the two examinations, and examinations of the same patient were performed by experienced but different cardiologists, who were blinded to each other’s diagnosis. The doctor who used the remote system was also randomly allocated and had not been previously specifically trained. The exams were real-time and diagnoses were made right after the exams. Results Of the 51 pts, the image quality was sufficient for diagnosis in 50 patients (48% female, 40±18 years). 1 pt was excluded because some key views could not be obtained using the remote system (98% of exams successful). 17 pts had positive findings, including 10 with a primary diagnosis of valvulopathy (1 Barlow's syndrome, 1 bicuspid aortic valve and 8 less-than-moderate regurgitation), 2 cardiac surgery follow-ups (1 case of aortic valve replacement and septal myectomy, and 1 case of mitral valve replacement and tricuspid annuloplasty), and 2 hypertrophic cardiomyopathy (including 1 case of obstruction at papillary muscle level), 2 with abnormal left ventricular wall motion(including 1 case of apical mural thrombus) (Figure 2), and 1 with congenital heart disease (secumdum atrial septal defect). The main diagnosis was consistent in 98% of cases (papillary muscle level obstruction was missed in one case), using conventional echocardiographic findings as the standard. Time for image acquision using remote echocardiography was significantly longer than conventional one (24 minutes 36 seconds ± 4 minutes 52 seconds vs. 16 minutes 15 seconds ± 1 minute 54 seconds, p<0.0001, paired t-test). Conclusions Comprehensive echocardiographic exam with a 5G cellular network and robotic arm-based remote system is feasible with relatively good diagnostic accuracy.Figure 1Figure 2

5G-Cloud-based real-time robotic part repairing for advanced manufacturing via computer vision

In this paper, we delve into the transformative capabilities of 5G wireless communication technology within the realm of robotics, particularly in the context of advanced manufacturing. Leveraging the power of computer vision and cloud/edge computing, we unveil the boundless possibilities that this technology heralds. Leveraging the ultra-reliable low latency communication (uRLLC) of 5G, we establish a distributed system showcasing its potential to revolutionize industrial processes. Additionally, to validate our framework, we developed a testbed tailored for real-world applications, focusing on milling operations using an industrial robot. Through high-level lidar data processing, we identify defects and create toolpaths, seamlessly to execute milling tasks. This research highlights 5G’s potential to redefine industrial processes while elucidating operational requirements for achieving uRLLC. Empirical testing underscores the benefits of 5G-robotics integration, enhancing efficiency and innovation in advanced manufacturing.

RoboMan: An Adult-Sized Humanoid Robot with Enhanced Performance, Inherent Stability, and Two-Stage Balance Control to Facilitate Research on Humanoids

Creating an adult-sized humanoid robot with stable walking capabilities is a major challenge in robotics. While many renowned research groups focus on robots for perilous work environments and precision tasks, our approach simplifies balance control, making it accessible to robotics research groups and educational institutes. This facilitates the development of complex functionalities such as vision and object manipulation for adult-sized humanoids. This research article introduces RoboMan II, an advanced version of RoboMan I, which won the most prestigious award in all humanoid robot leagues at RoboCup 2016 due to its exceptional performance in walking and playing soccer. RoboMan II features significant improvements in performance, inherent stability, recovery after falls, and balance control. To facilitate its development, RoboMan II is lighter and incorporates a modified foot and parallel structure for its leg to boost its inherent stability, along with a two-stage balance control system for Immediate Response and Gradual Adaptation, enhancing its adaptability in various environments. Our simulation results demonstrate that RoboMan II’s walking stability on flat surfaces improved significantly in the face of minor perturbations, with the number of steps within the stable region increasing from 24%, with only the immediate controller to 58% when both controllers were used. Similar improvements were observed on inclined surfaces. Additionally, the 3D CAD files for all of the robot parts are released as open source in conjunction with this paper to facilitate reproduction and further innovation. The forthcoming RoboMan III will incorporate custom servo motors for increased speed, torque, and enhanced fall recovery, preventing disengagement of the gear box after a fall. It promises to be an invaluable asset for research and practical applications in humanoid robotics.

Instrumented bio-inspired cable-driven compliant continuum robot: static modeling and experimental evaluation

Abstract Energy efficiency is inherent for autonomous robotic device. Snakes are well known for their ability to low energy consumption when swimming. However, the swimming know-how is poorly understood. Designing a snake robot inspired by snakes as a tool to find out the swimming energy efficiency crucial point will lead to the development of hyper efficient undulating locomotors. In this article, we introduce a four tendons driven continuum robot made of bio-inspired compliant vertebrae to assess the energy consumption of a planar and a spatial snake motion. The tendon-driven continuum robot constitutes the head–neck part of a locomotor snake robot. A static modeling coupled with an optimization method was implemented to generate bio-inspired motions recorded on snake swimming head. A friction model describing the friction between cables and the disks is investigated and compared to a frictionless model. The proposed prototype is equipped with exteroceptive sensors to record motion and proprioceptive sensors to measure cable forces applied at the tip of the robot. Hence, the work of the forces, thus the energy required to execute a trajectory are computed and analyzed. The energy is introduced as a key criterion to assess the swimming motion of a locomotor snake robot.

A robust low-friction triple network hydrogel based on multiple synergistic enhancement mechanisms

Hydrogels exhibit promising applications, particularly due to their high water content and excellent biocompatibility. Despite notable progress in hydrogel technology, the concurrent enhancement of water content, mechanical strength, and low friction poses substantial challenges to practical utilization. In this study, employing molecular and network design guided based on multiple synergistic enhancement mechanisms, we have developed a robust polyvinyl alcohol (PVA)–polyacrylic acid (PAA)–polyacrylamide (PAAm) three-network (TN) hydrogel exhibiting high water content, enhanced strength, low friction, and fatigue resistance. The hydrogel manifests a water content of 63.7%, compression strength of 6.3 MPa, compression modulus of 2.68 MPa, tensile strength reaching 7.3 MPa, and a tensile modulus of 10.27 MPa. Remarkably, even after one million cycles of dynamic loading, the hydrogel exhibits no signs of fatigue failure, with a minimal strain difference of only 1.15%. Furthermore, it boasts a low sliding coefficient of friction (COF) of 0.043 and excellent biocompatibility. This advancement extends the applications of hydrogels in emerging fields within biomedicine and soft bio-devices, including load-bearing artificial tissues, artificial blood vessels, tissue scaffolds, robust hydrogel coatings for medical devices, and joint parts of soft robots.

A Dataset for Detection and Segmentation of Underwater Marine Debris in Shallow Waters

Robust object detection is crucial for automating underwater marine debris collection. While supervised deep learning achieves state-of-the-art performance in discriminative tasks, replicating this success on underwater data is challenging. The generalization of these methods suffers due to a lack of available annotated data considering different sources of variation in the unstructured underwater environment and imaging conditions. In this paper, we present the Seaclear Marine Debris Dataset, the first publicly available shallow-water marine debris dataset annotated for instance segmentation/object detection. The dataset contains 8610 images collected using ROVs at multiple locations and with different cameras, annotated for 40 object categories, encompassing not only litter but also observed animals, plants, and robot parts. As part of the technical validation, we provide baseline results for object detection using Faster RCNN and YOLOv6 models. Furthermore, we demonstrate the non-triviality of generalizing the trained model performance to unseen sites and cameras due to domain shift. This underscores the value of the presented dataset in further developing robust models for underwater debris detection.

Efficient Path Planning in Medical Environments: Integrating Genetic Algorithm and Probabilistic Roadmap (GA-PRM) for Autonomous Robotics

Path-planning is a crucial part of robotics, helping robots move through challenging places all by themselves. In this paper, we introduce an innovative approach to robot path-planning, a crucial aspect of robotics. This technique combines the power of Genetic Algorithm (GA) and Probabilistic Roadmap (PRM) to enhance efficiency and reliability. Our method takes into account challenges caused by moving obstacles, making it skilled at navigating complex environments. Through merging GA's exploration abilities with PRM's global planning strengths, our GA-PRM algorithm improves computational efficiency and finds optimal paths. To validate our approach, we conducted rigorous evaluations against well-known algorithms including A*, RRT, Genetic Algorithm, and PRM in simulated environments. The results were remarkable, with our GA-PRM algorithm outperforming existing methods, achieving an average path length of 25.6235 units and an average computational time of 0.6881 seconds, demonstrating its speed and effectiveness. Additionally, the paths generated were notably smoother, with an average value of 0.3133. These findings highlight the potential of the GA-PRM algorithm in real-world applications, especially in crucial sectors like healthcare, where efficient path-planning is essential. This research contributes significantly to the field of path-planning and offers valuable insights for the future design of autonomous robotic systems.

Current Status of Patent Research on Picking End Effector

Background: Fruit and vegetable picking, as the most important part of fruit and vegetable production, is a labor-intensive industry. Fruit and vegetable picking robots can effectively improve the efficiency of picking and reduce labor requirements. As the most important part of the picking robot, the picking end-effector effectively plays a key role in improving the picking efficiency and ensuring the wholeness of the fruit. Therefore, the development trend of picking end effectors has received more and more attention. Objective: The study aimed to solve the problems of high labor consumption and low picking efficiency of manual picking; thus, the grasping method of the picking end effector has been continuously improved. Methods: This article has presented various representative patents related to the picking end effector, such as the suction end effector, multi-finger end effector, and bionic end effector. Results: Through the investigation of a large number of picking end effector patents, the current problems, such as low accuracy and large clamping damage, are summarized and analyzed. In addition, the future trends of fruit and vegetable picking end effectors are discussed. Conclusion: The optimization of the picking end effector is conducive to reducing manual labor and improving the picking rate of fruits and vegetables. More relevant patents will be invented in the future.

Intrinsic Permanent Shape Reconfigurable Semicrystalline Biopolyester Thermoset.

Catalyst-free, volatile organic solvent (VOC)-free synthesis of biobased cross-linked polymers is an important sustainable feature in polyesterification. To date, these polyesters have been extensively studied for their fundamental sustainability across various uses. The ultimate potential sustainability for these materials, however, is constrained to static structural parts due to their intractable rigid three-dimensional (3D) network. Here, we reveal intrinsic dynamic exchangeable bonds within this type of cross-linked semicrystalline network, poly(1,8-octanediol-co-1,12-docanedioate-co-citrate) (PODDC), enabling permanent shape reconfigurability. Annealing at slightly above melting-transition temperature (Tm) allows for shape reconfigurability up to nine times, comparable in performance to the existing bond-exchange systems. No reagents are involved from synthesis to shape reconfiguration, suggesting an exciting feature exhibited by this sustainable cross-linked material without the need for further chemical modification. We further extend this benefit of reconfigurability to enable flexible shape design in a smart shape-memory polymer (SMP), showing it as one of its potential applications. After its applications, it can undergo hydrolytic degradation. We envision that such multifaceted sustainability for the material will attract interest in environmentally friendly applications such as fabricating external part of soft robots and shape-morphing devices with reduced environmental impact.

Experimental investigation on enhancement in pure axial deformation of soft pneumatic actuator (SPA) with cap ring reinforcement

Bio-inspired soft-robots are nowadays found their place in many applications due to its flexibility, compliance and adaptivity to unstructured environment. The main intricate part of such bio-inspired soft robots are soft pneumatic actuators (SPA) which replicate or mimic the limbs and muscles. The soft actuators are pneumatically actuated and provide bending motion in most cases. However, many engineering and medical applications need axially expanding soft pneumatic actuators to deal with delicate objects. Various studies have put forward designs for SPA with axial deformation, but the majority of them have limited axial deformation, constraining motion and less overall efficacy which limit the scope of utilization. The common practice to enhance the axial deformation of SPA is by incorporating directionally customized reinforcement using fibres or by other means like yarns, fabrics, etc These types of reinforcements are generally embedded to SPA during fabrication and may not have capability for any correction or modification later on hence lack the customization. This paper presents a novel method of radial reinforcement for the enhancement of axial deformation of SPAs with provision of customization. The present study aims to enhance and/or customize the axial deformation of SPA by incorporating external and detachable reinforcement in the form of annulus shaped cap ring. The investigation encompasses the design and attachment of four distinct cap ring geometries to SPA at different locations. Experimental results affirm that cap ring reinforcement bolster the radial stiffness, curbing lateral deformation while permitting axial deformation of soft pneumatic actuators. Out of 64 distinct configurations, the one with full reinforcement, featuring four cap rings of maximum size, yields a remarkable 169% increase in pure axial deformation compared to unreinforced cases. It is also observed that by varying the number and placement locations of cap rings the pure axial deformation can be customized. This novel insight not only propels soft pneumatic actuation technology but also heralds prospects for highly agile and versatile robotic systems which can be used in medical, prosthetics, pharmaceutical and other industries.

Parameter Calibration of Discrete Element Model of Wine Lees Particles

In order to investigate the contact characteristics of the mechanical parts of the brewing robot with wine lees particles, it is essential to calibrate the parameters of the discrete elemental model of wine lees particles. This paper proposes a method based on tests of the angle of repose. The simulation test is conducted to establish a regression model and combined with physical tests to find optimization. The contact model used in simulation modeling is Hertz-Mindlin with Johnson-Kendall-Roberts. Not all discrete element model parameters of wine lees particles have a significant impact on the angle of repose, so screening through Plackett-Burman Design is performed. The results indicate that the restitution coefficient between wine lees particles and restitution coefficient between wine lees particle and steel plate have a significant impact on angle of repose. Additionally, another parameter that is difficult to obtain, namely surface energy (JKR), also plays a crucial role. The optimal value interval for these three parameters is determined by the steepest ascent test, and a linear regression model for angle of repose is built through Box-Behnken Design. The optimal values obtained are as follows: restitution coefficient between wine lees particles—0.603; restitution coefficient between wine lees particle and steel plate—0.595; JKR—0.083. Finally, in order to verify the accuracy of calibrated parameters, simulation verification tests are carried out which show that there is only a relative error rate at 0.18% between simulated angle of repose and actual angle of repose, indicating that accurate calibration parameters were achieved. This study can provide reference for selecting discrete element model parameters for wine lees particles in future research endeavors.

Design and Construction of 3 DOF Prototype Delta Parallel Robot

Abstract: The design and construction of a prototype delta robot to utilize for upper secondary educational institutes is presented. The focus is on leveraging 3D printing technology in AutoCAD for component fabrication, detailing electrical schematics, and integrating Arduino for its intuitive User Interface (UI). The project’s objective is to construct a delta robot prototype equipped with essential features to serve as an educational tool for teaching fundamental robotics principles. Additionally, the design allows for customization of specific robot parts in future iterations to adapt it to various applications as needed

A Review and Evaluation of Control Architectures for Modular Legged and Climbing Robots.

Robotic control is a fundamental part of autonomous robots. Modular legged and climbing robots are complex machines made up of a variety of subsystems, ranging from a single robot with simple legs to a complex system composed of multiple legs (or modules) with computing power and sensitivity. Their complexity, which is increased by the fact of needing elements for climbing, makes a correct structure crucial to achieve a complete, robust, and versatile system during its operation. Control architectures for legged robots are distinguished from other software architectures because of the special needs of these systems. In this paper, we present an original classification of modular legged and climbing robots, a comprehensive review of the most important control architectures in robotics, focusing on the control of modular legged and climbing robots, and a comparison of their features. The control architecture comparison aims to provide the analytical tools necessary to make informed decisions tailored to the specific needs of your robotic applications. This article includes a review and classification of modular legged and climbing robots, breaking down each category separately.

Sexuality in the era of transhumanism: A point of view

AbstractSeveral technological and scientific developments have arisen to enhance the human condition. Transhumanism is an intellectual movement that gathers different knowledge sectors to attain a physical and psychological fullness state, with capacities that surpass a human as is known today. These advances have led to a remarkable development in human–robot interaction, an interaction science that studies how technology could influence human behavior. Social robots are part of this science, looking to improve the interaction between robots and the general population in everyday contexts. Sex robots, being part of social robots, have gained a lot of importance in the industry. But, does any relationship exist between transhumanism and sexuality? Some authors have proposed beneficial sex robots in sexual dysfunctions and older adults. However, several contradictors state that sex robots will not be helpful, but they may aggravate these conditions. Further studies are needed to assess the real impact of these devices on sexual dysfunctions, as lack of evidence prevents firmly recommending them as part of treatment protocols.

Characterization of Exterior Parts for 3D-Printed Humanoid Robot Arm with Various Patterns and Thicknesses.

Currently, metal is the most common exterior material used in robot development due to the need to protect the motor. However, as soft, wearable, and humanoid robots are gradually being developed, many robot parts need to be converted into artificial skin using flexible materials. In this study, in order to develop soft exterior parts for robots, we intended to manufacture exterior robot arm parts via fused filament fabrication (FFF) 3D printing according to various structural and thickness conditions and analyze their mechanical properties. The exterior parts of the robot arms were manufactured utilizing Shore 95 A TPU (eTPU, Esun, Shenzhen, China), which is renowned for its softness and exceptional shock absorption characteristics. The exterior robot arm parts were modeled in two parts, the forearm and upper arm, by applying solid (SL) and re-entrant (RE) structures and thicknesses of 1, 2, and 4 mm. The mechanical properties were analyzed through the use of three-point bending, tensile, and compression testing. All of the characterizations were analyzed using a universal testing machine (AGS-X, SHIMADZU, Kyoto, Japan). After testing the samples, it was confirmed that the RE structure was easily bendable towards the bending curve and required less stress. In terms of the tensile tests, the results were similar to the bending tests; to achieve the maximum point, less stress was required, and for the compression tests, the RE structure was able to withstand the load compared to the SL structure. Therefore, after analyzing all three thicknesses, it was confirmed that the RE structure with a 2 mm thickness had excellent characteristics in terms of bending, tensile, and compressive properties. Therefore, the re-entrant pattern with a 2 mm thickness is more suitable for manufacturing a 3D-printed humanoid robot arm.

Service robotics

All robotics can be divided into two large parts: industrial and service. Industrial robotics is used in industrial production, mainly in mechanical engineering, while service robotics allows for assistance in serving people. If the first part of robotics is close to saturation, then the second service part has a huge diverse development potential with large numbers of unfilled niches, many of which do not require large capital investments. One such niche is artificial intelligence. To create it, you need highly qualified programmers — developers and the availability of computer equipment, which has an impact on reducing prices. The reduction in the cost of computer components leads to the fact that the number of different sensors connected to each other via the Internet continues to grow, which, in turn, makes it possible to create a lot of smart kitchen appliances. But robotics' biggest service success is in medicine and healthcare. Robotics is used in surgery, diagnostics, patient care, and disinfection. Much progress has been made in the creation of chatbots. Robot consultants, robot waiters, robot cashiers, robot secretaries are constantly used. The development of robotics in Russia has great prospects. Russia has a developed engineering school, a technocratic society, and a positive attitude towards robots. But there are also weaknesses. Poor migration policy and protection of social security of the population lead to a large flow of unskilled migrants into the country. A robot can do everything except one thing — replace a migrant worker, especially when employers have no interest in such a replacement. This approach greatly reduces the intellectual level of production and leads to Russia's technological lag behind the implementation of other countries. Russia has all the prerequisites to make a qualitative leap in the development of service robotics and achieve results in this industry at the forefront.

Combined Soft Grasping and Crawling Locomotor Robot for Exterior Navigation of Tubular Structures

This paper presents the design, development, and testing of a robot that combines soft-body grasping and crawling locomotion to navigate tubular objects. Inspired by the natural snakes’ climbing locomotion of tubular objects, the soft robot includes proximal and distal modules with radial expansion/contraction for grasping around the objects and a longitudinal contractile–expandable driving module in-between for providing a bi-directional crawling movement along the length of the object. The robot’s grasping modules are made of fabrics, and the crawling module is made of an extensible pneumatic soft actuator (ePSA). Conceptual designs and CAD models of the robot parts, textile-based inflatable structures, and pneumatic driving mechanisms were developed. The mechanical parts were fabricated using advanced and conventional manufacturing techniques. An Arduino-based electro-pneumatic control board was developed for generating cyclic patterns of grasping and locomotion. Different reinforcing patterns and materials characterize the locomotor actuators’ dynamical responses to the varying input pressures. The robot was tested in a laboratory setting to navigate a cable, and the collected data were used to modify the designs and control software and hardware. The capability of the soft robot for navigating cables in vertical, horizontal, and curved path scenarios was successfully demonstrated. Compared to the initial design, the forward speed is improved three-fold.

Measurements of Electrodermal Activity, Tissue Oxygen Saturation, and Visual Analog Scale for Different Cuff Pressures.

The quantification of comfort in binding parts, essential human-machine interfaces (HMI) for the functioning of rehabilitation robots, is necessary to reduce physical strain on the user despite great achievements in their structure and control. This study aims to investigate the physiological impacts of binding parts by measuring electrodermal activity (EDA) and tissue oxygen saturation (StO2). In Experiment 1, EDA was measured from 13 healthy subjects under three different pressure conditions (10, 20, and 30 kPa) for 1 min using a pneumatic cuff on the right thigh. In Experiment 2, EDA and StO2 were measured from 10 healthy subjects for 5 min. To analyze the correlation between EDA parameters and the decrease in StO2, a survey using the visual analog scale (VAS) was conducted to assess the level of discomfort at each pressure. The EDA signal was decomposed into phasic and tonic components, and the EDA parameters were extracted from these two components. RM ANOVA and a post hoc paired t-test were used to determine significant differences in parameters as the pressure increased. The results showed that EDA parameters and the decrease in StO2 significantly increased with the pressure increase. Among the extracted parameters, the decrease in StO2 and the mean SCL proved to be effective indicators. Such analysis outcomes would be highly beneficial for studies focusing on the comfort assessment of the binding parts of rehabilitation robots.

Multi-objective design optimization of an in-pipe inspection robot

In addition to inspection, In-Pipe Inspection Robots (IPIRs) could be enabled to perform other tasks, such as object retrieval and blockage clearing. In this study, a new IPIR is proposed with a design aimed at expanding its range of potential applications beyond inspection. The design methodology followed to facilitate the aforementioned application expansion commences with the development of a parametric preliminary design of an IPIR, in which the sizing of the robot parts are determined based on an optimization problem formulated in this work. The multi-objective optimization problem maximizes two contradictory objective functions, namely, its payload capacity, and the range of pipe diameters in which it can fit (radial range). The problem's Pareto front is solved using the NSGA-II implemented by Matlab's gamultiobj(.). The robot's final design is selected based on one of the Pareto-optimal solutions obtained from the Pareto front with a theoretical payload capacity of 11 kg and a radial range of 33 mm. The robot was manufactured and tested to validate such theoretical results.