In this paper a new family of companion forms associated to a regular polynomial matrix is presented. Similar results have been presented in a recent paper by M. Fiedler, where the scalar case is considered. It is shown that the new family of companion forms preserves both the finite and infinite elementary divisors structure of the original polynomial matrix, thus all its members can be seen as linearizations of the corresponding polynomial matrix. Furthermore, for the special class of self-adjoint polynomial matrices a particular member is shown to be self-adjoint itself.

Robots have become a popular educational tool in secondary education, introducing scientific, technological, engineering and mathematical concepts to students all around the globe. In this paper EUROPA, an extensible, open software and open hardware robotic platform is presented focusing on teaching physics, sensors, data acquisition and robotics. EUROPA’s software infrastructure is based οn Robot Operating System (ROS). It includes easy to use interfaces for robot control and interaction with users and thus can easily be incorporated in Science, Technology, Engineering and Mathematics (STEM) and robotics classes. EUROPA was designed taking into account current trends in educational robotics. An overview of widespread robotic platforms is presented, documenting several critical parameters of interest such as their architecture, sensors, actuators and controllers, their approximate cost, etc. Finally, an introductory STEM curriculum developed for EUROPA and applied in a class of high school students is presented.

Artificial intelligence (AI) and machine learning (ML) are pursued in most fields of data analysis, and have already become a part of everyday applications. As AI and ML are an integral part of the Industry 4.0 era, it becomes necessary to introduce a basic understanding of what AI and ML means and how it can be applied in K–12 education. Although educators need to prepare for this revolution, it is generally admitted that there is a shortage of suitable tools and methods toward this goal. In this article, we propose that it is necessary to design courses for machine learning using STEM-based robotic tools. We present selected robotic kits with ML capabilities that can be used to target concepts of machine learning in K–12 classrooms. Finally, we present our own conceptual rules on how constructivist educational robotics with AI capabilities can effectively support teaching scenarios in future K–12 curricula.