2. Universidad Cardenal Herrera-CEU

This document aims to make a retrospective of our work in the Ford research group in collaboration with researchers from the CEU Cardenal Herrera University and the University of Valencia. The research group originated from the doctoral thesis by Eduardo García Magraner and his thesis was directed by Nicolás Montés in 2016. The Mini-terms were formulated for the first time in this thesis. From then on, the research group grew as the mini-terms began to consolidate both industrially and scientifically. At industrial level we were provided with a CDTI (Centre for the Development of Industrial Technology) which made it possible to massify the mini-terms at Ford factory in Valencia and at scientific level we attended different congresses. Especially relevant was ICINCO 2018 since the concept of the mini-terms could be presented to the programme chair of the congress, Oleg Gusikhin, (Global Data Insight & Analytics, Ford Motor Company, United States). His support led to the consolidation of the mini-terms through their standardization within Ford and also the consolidation of the group through the inclusion of the CEU Cardenal Herrera University in the URP (University Research Program). The success of Eduardo García’s doctoral thesis motivated the Foundation for Development and Innovation (FDI) to decide to fund doctoral theses within Ford, financing a thesis in collaboration with the University of Valencia and another one with the CEU Cardenal Herrera University. Moreover, Eduardo García’s thesis motivated the staff of the plant to take the step to carry out doctoral theses, funded by the INNODOCTO programme of the Generalitat Valenciana. Throughout this journey different awards have been won such as the Henry Ford Technology Awards in 2019, the Factories of the Future Awards in 2021, the Global Manufacturing Technical Excellence Award in 2023 and the Angel Herrera Award for the best research work in 2024. Twenty-four communications have been made to congresses, ICINCO being the congress with the highest number of communications. In particular, at ICINCO 2020, one of these articles was selected as the Best Industrial Paper Award. Thirteen articles have been published in indexed journals with an impact index and also three book chapters. This document aims at reviewing the different tools and concepts developed and introduced by the research group as well as trying to define its objective.

Históricamente, entre los estudiantes que llegan a la educación superior existe un alto grado de percepción negativa sobre la incidencia en la creatividad que tienen las asignaturas propedéuticas como matemáticas o física. Esta afirmación se hace más evidente entre aquellos alumnos que deciden cursar estudios donde convide la adquisición de competencias para desarrollar procesos creativos y la integración de las asignaturas de carácter técnico, lo que se traduce en la dificultad de asimilar la interrelación de ambas partes. Esta situación tiene gran incidencia en estudios superiores como Arquitectura o Ingeniería en Diseño Industrial, donde los alumnos se mueven en equilibrio entre áreas creativas como dibujo o proyectos, y otras más científicas o técnicas, como física o estructuras. Con la intención de romper este habito y promover que el alumno entienda que las asignaturas propedéuticas pueden llegar a formar parte del propio proceso creativo de un proyecto, se ha iniciado una actividad en el Grado de Fundamentos de Arquitectura en la Universidad CEU-Cardenal Herrera, que pretenden fomentar un cambio en la percepción negativa de estas áreas. Mediante esta comunicación, se pretende mostrar una de estas actividades que ha consistido en la participación de los alumnos del primer curso de Arquitectura en un concurso internacional de diseño como actividad motivadora y que, como premisa de partida, la idea generadora del proyecto debe de basarse en un concepto matemático o físico. En definitiva, cambiar la percepción histórica y negativa de que los conceptos adquiridos en asignaturas básicas, no pueden formar parte del proceso creativo del proyecto.

Vocation is one of the determining factors taken into account by students when choosing their university studies. However, when the students start their studies, in their first year, they will find a series of basic subjects that barely motivate or stimulate them. In the specific case of mathematics, the problem is aggravated when many of the students already begin the first year showing rejection towards this subject. The lack of motivation for mathematics also affects the subject of physics because “the role of mathematics is to be the language of physics”. The EXPLORIA project proposed by the CEU Cardenal Herrera University is a potential solution to this problem. The objective of this project is the implementation of STEAM learning (Science Technology Engineering Art Mathematics) in the Degree in Fundamentals of Architecture at CEU Cardenal Herrera University through the EXPLORIA project. This article focuses on the activities carried out in the subject of physics in the Degree in Fundamentals of Architecture, corresponding to the part of mechanical engineering in order to show that through the realization of different challenges, we can develop creative products, new buildings with their logos and storytelling, as well as connect with the rest of subjects. For its development, students must use everyday objects within their reach, such as forks, spoons, knives, shoes, etc., to build an object or structure that must remain in a “creative balance” and this will serve as an inspiration for new buildings. These new creations are evaluated by an architecture team who fills in a rubric to evaluate the creativity and originality of the products. The number of students included in this project was 24 and the participants’ age ranged between 18 and 20 (similarly distributed). At the end of the work, an anonymous ad hoc questionnaire was carried out to show the students’ assessment of the new teaching methodology and the challenges developed in the subject of physics.

Our society is immersed in the Fourth Industrial Revolution due to the fast evolution of the new technologies that are modifying the labor market. In the near future, technologies related to Industry 4.0 will produce totally new goods and services. Therefore, the educational systems should adapt their programs to the future needs of an uncertain labor market. In particular, mathematics will play a key role in future jobs and there is a strong need to connect its teaching methodologies to the new technological scene. This work uses the STEAM approach (science, technology, engineering, arts and mathematics) along with active methodologies and educational robotics with the aim of developing a new strategy for the application of mathematics and physics in an engineering degree. In particular, a transportation challenge is posed to tackle the teaching–learning process of the Bézier curves and their applications in physics. A pilot project is developed using a LEGO EV3 robot and an active methodology, where students become the center of the learning process. The experimental results of the pilot study indicate an increase in the motivation due to the use of robots and the realistic context of the challenge.

This article defines a new concept for real-time factory management—manufacturing maps. Manufacturing maps are generated from two fundamental elements, mini-terms and Petri nets. Mini-terms are sub-times of a technical cycle, the time it takes for any component to perform its task. A mini-term, by definition, is a sub-cycle time and it would only make sense to use the term in connection with production improvement. Previous studies have shown that when the sub-cycle time worsens, this indicates that something unusual is happening, enabling anticipation of line failures. As a result, a mini-term has dual functionality, since, on the one hand, it is a production parameter and, on the other, it is a sensor used for predictive maintenance. This, combined with how easy and cheap it is to extract relevant data from manufacturing lines, has resulted in the mini-term becoming a new paradigm for predictive maintenance, and, indirectly, for production analysis. Applying this parameter using big data for machines and components can enable the complete modeling of a factory using Petri nets. This article presents manufacturing maps as a hierarchical construction of Petri nets in which the lowest level network is a temporary Petri net based on mini-terms, and in which the highest level is a global view of the entire plant. The user of a manufacturing map can select intermediate levels, such as a specific production line, and perform analysis or simulation using real-time data from the mini-term database. As an example, this paper examines the modeling of the 8XY line, a multi-model welding line at the Ford factory in Almussafes (Valencia), where the lower layers are modeled until the mini-term layer is reached. The results, and a discussion of the possible applications of manufacturing maps in industry, are provided at the end of this article.

Over the last years, mobile robot platforms are having a key role in education worldwide. Among others, LEGO Robots and MATLAB/Simulink are being used mainly in universities to improve the teaching experience. Most LEGO systems used in the literature are based on NXT, as the EV3 version is relatively recent. In contrast to the previous versions, the EV3 allows the development of real-time applications for teaching a wide variety of subjects as well as conducting research experiments. The goal of the research presented in this paper was to develop and validate a novel real-time educational platform based on the MATLAB/Simulink package and the LEGO EV3 brick for academic use in the fields of robotics and computer science. The proposed framework is tested here in different university teaching situations and several case studies are presented in the form of interactive projects developed by students. Without loss of generality, the platform is used for testing different robot path planning algorithms. Classical algorithms like rapidly-exploring random trees or artificial potential fields, developed by robotics researchers, are tested by bachelor students, since the code is freely available on the Internet. Furthermore, recent path planning algorithms developed by the authors are also tested in the platform with the aim of detecting the limits of its applicability. The restrictions and advantages of the proposed platform are discussed in order to enlighten future educational applications.

This paper presents a real-time global path planning method for mobile robots using harmonic functions, such as the Poisson equation, based on the Proper Generalized Decomposition (PGD) of these functions. The main property of the proposed technique is that the computational cost is negligible in real-time, even if the robot is disturbed or the goal is changed. The main idea of the method is the off-line generation, for a given environment, of the whole set of paths from any start and goal configurations of a mobile robot, namely the computational vademecum, derived from a harmonic potential field in order to use it on-line for decision-making purposes. Up until now, the resolution of the Laplace or Poisson equations has been based on traditional numerical techniques unfeasible for real-time calculation. This drawback has prevented the extensive use of harmonic functions in autonomous navigation, despite their powerful properties. The numerical technique that reverses this situation is the Proper Generalized Decomposition. To demonstrate and validate the properties of the PGD-vademecum in a potential-guided path planning framework, both real and simulated implementations have been developed. Simulated scenarios, such as an L-Shaped corridor and a benchmark bug trap, are used, and a real navigation of a LEGO®MINDSTORMS robot running in static environments with variable start and goal configurations is shown. This device has been selected due to its computational and memory-restricted capabilities, and it is a good example of how its properties could help the development of social robots.

A novel algorithm called the Proper Generalized Decomposition (PGD) is widely used by the engineering community to compute the solution of high dimensional problems. However, it is well-known that the bottleneck of its practical implementation focuses on the computation of the so-called best rank-one approximation. Motivated by this fact, we are going to discuss some of the geometrical aspects of the best rank-one approximation procedure. More precisely, our main result is to construct explicitly a vector field over a low-dimensional vector space and to prove that we can identify its stationary points with the critical points of the best rank-one optimization problem. To obtain this result, we endow the set of tensors with fixed rank-one with an explicit geometric structure.

A necessity in the design of a path planning algorithm is to account for the environment. If the movement of the mobile robot is through a dynamic environment, the algorithm needs to include the main constraint: real-time collision avoidance. This kind of problem has been studied by different researchers suggesting different techniques to solve the problem of how to design a trajectory of a mobile robot avoiding collisions with dynamic obstacles. One of these algorithms is the artificial potential field (APF), proposed by O. Khatib in 1986, where a set of an artificial potential field is generated to attract the mobile robot to the goal and to repel the obstacles. This is one of the best options to obtain the trajectory of a mobile robot in real-time (RT). However, the main disadvantage is the presence of deadlocks. The mobile robot can be trapped in one of the local minima. In 1988, J.F. Canny suggested an alternative solution using harmonic functions satisfying the Laplace partial differential equation. When this article appeared, it was nearly impossible to apply this algorithm to RT applications. Years later a novel technique called proper generalized decomposition (PGD) appeared to solve partial differential equations, including parameters, the main appeal being that the solution is obtained once in life, including all the possible parameters. Our previous work, published in 2018, was the first approach to study the possibility of applying the PGD to designing a path planning alternative to the algorithms that nowadays exist. The target of this work is to improve our first approach while including dynamic obstacles as extra parameters.