A new meta-module for efficient reconfiguration of hinged-units modular robots

We present a robust and compact meta-module for edge-hinged modular robot units such as M-TRAN, SuperBot, SMORES, UBot, PolyBot and CKBot, as well as for central-point-hinged ones such as Molecubes and Roombots. Thanks to the rotational degrees of freedom of these units, the novel meta-module is able to expand and contract, as to double/halve its length in each dimension. Moreover, for a large class of edge-hinged robots the proposed meta-module also performs the scrunch/relax and transfer operations required by any tunneling-based reconfiguration strategy, such as those designed for Crystalline and Telecube robots. These results make it possible to apply efficient geometric reconfiguration algorithms to this type of robots. We prove the size of this new meta-module to be optimal. Its robustness and performance substantially improve over previous results.Peer ReviewedPostprint (author's final draft

Mudanças no financiamento da saúde no contexto de descentralização da saúde: o caso de três países latino-americanos

OBJECTIVE: The results of an evaluative longitudinal study, which identified the effects of health care decentralization on health financing in Mexico, Nicaragua and Peru are presented in this article. METHODS: The methodology had two main phases. In the first, secondary sources of data and documents were analyzed with the following variables: type of decentralization implemented, source of financing, funds for financing, providers, final use of resources, mechanisms for resource allocation. In the second phase, primary data were collected by a survey of key personnel in the health sector. RESULTS: Results of the comparative analysis are presented, showing the changes implemented in the three countries, as well as the strengths and weaknesses of each country in matters of financing and decentralization. CONCLUSIONS: The main financing changes implemented and quantitative trends with respect to the five financing indicators are presented as a methodological tool to implement corrections and adjustments in health financing.OBJETIVO: São apresentados os resultados de um estudo longitudinal com o objetivo de identificar os efeitos da descentralização nas políticas de financiamento em três países da América Latina: México, Nicarágua e Peru. MÉTODOS: A metodologia teve duas fases principais. Na primeira, foram analisadas as fontes de dados secundários, referentes às seguintes variáveis: tipo de descentralização implementada, fontes de financiamento, provedores de serviços, mecanismos de alocação de recursos e destino final de recursos. Na segunda fase, foram analisadas as fontes de dados primários obtidos por meio de entrevistas diretas com pessoal-chave do setor de saúde, tomando como guia as mesmas variáveis da primeira etapa. RESULTADOS: Os resultados identificaram as fortalezas e as debilidades de cada país em matéria de políticas de financiamento e de descentralização. CONCLUSÕES: As principais mudanças no financiamento, assim como as tendências quantitativas dos cinco indicadores de financiamento utilizados, são apresentadas como instrumento metodológico para implementar correções e ajustes do financiamento em saúde

A new meta-module design for efficient reconfiguration of modular robots

This is a post-peer-review, pre-copyedit version of an article published in Autonomous Robots. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10514-021-09977-6We propose a new meta-module design for two important classes of modular robots. The new metamodule is three-dimensional, robust and compact, improving on the previously proposed one. It applies to socalled “edge-hinged” modular robot units, such as MTRAN, SuperBot, SMORES, UBot, PolyBot and CKBot, as well as to so-called “central-point-hinged” modular robot units, which include Molecubes and Roombots. The new meta-module uses the rotational degrees of freedom of these two types of robot units in order to expand and contract, as to double or halve its length in each of the two directions of its three dimensions, therefore simulating the capabilities of Crystalline and Telecube robots. Furthermore, in the edge-hinged case we prove that the novel meta-module can also perform the scrunch, relax and transfer moves that are necessary in any tunnelingbased reconfiguration algorithm for expanding/contracting modular robots such as Crystalline and Telecube. This implies that the use of meta-meta-modules is unnecessary, and that currently existing efficient reconfiguration algorithms can be applied to a much larger set of modular robots than initially intended.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 734922. I.P. was supported by the Austrian Science Fund (FWF): W1230. V.S. and R.S. were supported by projects MINECO MTM2015-63791-R and Gen. Cat. 2017SGR1640. R.S. was also supported by MINECO through the Ram´on y Cajal program.Peer ReviewedPostprint (published version

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

Shooting Stars in Simple Drawings of Km,nK_{m,n}

Simple drawings are drawings of graphs in which two edges have at most one common point (either a common endpoint, or a proper crossing). It has been an open question whether every simple drawing of a complete bipartite graph $K_{m,n}$ contains a plane spanning tree as a subdrawing. We answer this question to the positive by showing that for every simple drawing of $K_{m,n}$ and for every vertex $v$ in that drawing, the drawing contains a shooting star rooted at $v$, that is, a plane spanning tree containing all edges incident to $v$.Comment: Appears in the Proceedings of the 30th International Symposium on Graph Drawing and Network Visualization (GD 2022

Crossing-Optimal Extension of Simple Drawings

In extension problems of partial graph drawings one is given an incomplete drawing of an input graph G and is asked to complete the drawing while maintaining certain properties. A prominent area where such problems arise is that of crossing minimization. For plane drawings and various relaxations of these, there is a number of tractability as well as lower-bound results exploring the computational complexity of crossing-sensitive drawing extension problems. In contrast, comparatively few results are known on extension problems for the fundamental and broad class of simple drawings, that is, drawings in which each pair of edges intersects in at most one point. In fact, the extension problem of simple drawings has only recently been shown to be NP-hard even for inserting a single edge. In this paper we present tractability results for the crossing-sensitive extension problem of simple drawings. In particular, we show that the problem of inserting edges into a simple drawing is fixed-parameter tractable when parameterized by the number of edges to insert and an upper bound on newly created crossings. Using the same proof techniques, we are also able to answer several closely related variants of this problem, among others the extension problem for k-plane drawings. Moreover, using a different approach, we provide a single-exponential fixed-parameter algorithm for the case in which we are only trying to insert a single edge into the drawing

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