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.

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a b s t r a c tThe Proper Generalized Decomposition or, for short, PGD is a tensor decomposition based technique to solve PDE problems. It reduces calculation and storage cost drastically and presents some similarities with the Proper Orthogonal Decomposition, for short POD. In this work, we propose an efficient implementation to improve the convergence of the PGD, toward the numerical solution of a discretized PDE problem, when the associated matrix is Laplacian-like.

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