Systematic strategies for 3-dimensional modular robots

Modular robots have been studied an classified from different perspectives, generally focusing on the mechatronics. But the geometric attributes and constraints are the ones that determine the self-reconfiguration strategies. In two dimensions, robots can be geometrically classified by the grid in which their units are arranged and the free cells required to move a unit to an edge-adjacent or vertex-adjacent cell. Since a similar analysis does not exist in three dimensions, we present here a systematic study of the geometric aspects of three-dimensional modular robots. We find relations among the different designs but there are no general models, except from the pivoting cube one, that lead to deterministic reconfiguration plans. In general the motion capabilities of a single module are very limited and its motion constraints are not simple. A widely used method for reducing the complexity and improving the speed of reconfiguration plans is the use of meta-modules. We present a robust and compact meta-module of M-TRAN and other similar robots that is able to perform the expand/contract operations of the Telecube units, for which efficient reconfiguration is possible. Our meta-modules also perform the scrunch/relax and transfer operations of Telecube meta-modules required by the known reconfiguration algorithms. These reduction proofs make it possible to apply efficient geometric reconfiguration algorithms to this type of robots

How to fit a tree in a box

We study compact straight-line embeddings of trees. We show that perfect binary trees can be embedded optimally: a tree with n nodes can be drawn on a vn by vn grid. We also show that testing whether a given rooted binary tree has an upward embedding with a given combinatorial embedding in a given grid is NP-hard.Peer ReviewedPostprint (author's final draft

Inserting one edge into a simple drawing is hard

A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G + e extending D(G). As a result of Levi’s Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP-complete to decide whether one edge can be inserted into a simple drawing. This remains true even if we assume that the drawing is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles. On the positive side, we show that, given an arrangement of pseudocircles A and a pseudosegment s, it can be decided in polynomial time whether there exists a pseudocircle Fs extending s for which A ¿ {Fs} is again an arrangement of pseudocircles.Peer ReviewedPostprint (published version

Systematic strategies for 3-dimensional modular robots

Modular robots have been studied an classified from different perspectives, generally focusing on the mechatronics. But the geometric attributes and constraints are the ones that determine the self-reconfiguration strategies. In two dimensions, robots can be geometrically classified by the grid in which their units are arranged and the free cells required to move a unit to an edge-adjacent or vertex-adjacent cell. Since a similar analysis does not exist in three dimensions, we present here a systematic study of the geometric aspects of three-dimensional modular robots. We find relations among the different designs but there are no general models, except from the pivoting cube one, that lead to deterministic reconfiguration plans. In general the motion capabilities of a single module are very limited and its motion constraints are not simple. A widely used method for reducing the complexity and improving the speed of reconfiguration plans is the use of meta-modules. We present a robust and compact meta-module of M-TRAN and other similar robots that is able to perform the expand/contract operations of the Telecube units, for which efficient reconfiguration is possible. Our meta-modules also perform the scrunch/relax and transfer operations of Telecube meta-modules required by the known reconfiguration algorithms. These reduction proofs make it possible to apply efficient geometric reconfiguration algorithms to this type of robots

Systematic strategies for 3-dimensional modular robots

Modular robots have been studied an classified from different perspectives, generally focusing on the mechatronics. But the geometric attributes and constraints are the ones that determine the self-reconfiguration strategies. In two dimensions, robots can be geometrically classified by the grid in which their units are arranged and the free cells required to move a unit to an edge-adjacent or vertex-adjacent cell. Since a similar analysis does not exist in three dimensions, we present here a systematic study of the geometric aspects of three-dimensional modular robots. We find relations among the different designs but there are no general models, except from the pivoting cube one, that lead to deterministic reconfiguration plans. In general the motion capabilities of a single module are very limited and its motion constraints are not simple. A widely used method for reducing the complexity and improving the speed of reconfiguration plans is the use of meta-modules. We present a robust and compact meta-module of M-TRAN and other similar robots that is able to perform the expand/contract operations of the Telecube units, for which efficient reconfiguration is possible. Our meta-modules also perform the scrunch/relax and transfer operations of Telecube meta-modules required by the known reconfiguration algorithms. These reduction proofs make it possible to apply efficient geometric reconfiguration algorithms to this type of robots

Experiencias de Aprendizaje-Servicio en la UPM: 2021 y 2022

La Oficina de Aprendizaje-Servicio (ApS) de la UPM, constituida en sesión del Consejo de Gobierno de diciembre de 2019 tiene, como misión fundamental, promover en el ámbito de las enseñanzas de esta universidad la metodología ApS. Con esta finalidad se vienen realizando convocatorias de proyectos de impacto social alineados con los ODS como un mecanismo más para la contribución a la Agenda 2030, y se colabora intensamente con las diversas oficinas constituidas con el mismo objetivo en otras universidades. Nuestra oficina pretende impulsar progresivamente la colaboración con entidades ajenas a la UPM, y atender demandas y necesidades sociales en las que nuestros estudiantes y profesores brinden sus conocimientos para la construcción de una mejor y más justa sociedad. Con este propósito, se han puesto en marcha numerosas iniciativas y colaboraciones con Ayuntamientos, Asociaciones, ONG, Fundaciones y centros de enseñanza, con el fin común de plantear mejoras y trabajar con entornos desfavorecidos, y colectivos vulnerables de nuestro entorno. Cabe destacar la muy positiva acogida que, progresivamente se está logrando, en lo relativo a la diseminación de estas iniciativas en el ámbito de la UPM, viéndose incrementada la participación e interés de nuestros docentes y estudiantes en los llamamientos que se realizan desde la oficina. Desde la constitución de la oficina, son ya más de 100 actividades desarrolladas con la participación de más de 500 profesores. Uno de los compromisos de la Oficina ApS de la UPM es dar visibilidad por su carácter meritorio a las experiencias realizadas por el profesorado y los estudiantes de nuestra universidad y, es por ello, que nos complace la presentación de esta primera edición del ebook, en el que se recogen algunas de las experiencias realizadas en nuestra universidad y que confiamos ampliar periódicamente con futuras ediciones. Nuestro más sincero agradecimiento a todos los profesores que habéis hecho posible esta primera publicación con vuestras contribuciones