DSpace Collection:
http://hdl.handle.net/2117/3199
2014-09-30T20:21:31ZSoftware using the Gröbner cover for geometrical loci computation and classification
http://hdl.handle.net/2117/24171
Title: Software using the Gröbner cover for geometrical loci computation and classification
Authors: Abanades, Miguel A.; Botan, Francisco; Montes Lozano, Antonio; Recio Muñiz, Tomás
Abstract: We describe here a properly recent application of the Gröbner Cover algorithm (GC) providing an algebraic support to Dynamic Geometry computations of geometrical loci. It provides a complete algebraic solution of locus computation as well as a suitable taxonomy allowing to distinguish the nature of the different components. We included a new algorithm Locus into the Singular grobcov.lib library for this purpose. A web prototype has been implemented using it in Geogebra.2014-09-26T08:32:28ZThe degree-diameter problem in maximal bipartite planar graphs
http://hdl.handle.net/2117/24097
Title: The degree-diameter problem in maximal bipartite planar graphs
Authors: Dalfó Simó, Cristina; Huemer, Clemens; Salas, Julian
Abstract: The (A ,D) (degree/diameter) problem consists of finding the largest possible number of vertices n among all the graphs with maximum degree and diameter D. We consider the (A ,D) problem for maximal planar bipartite graphs, that are simple planar graphs in which every face is a quadrangle. We obtain that for the ( , 2) problem, the number of vertices is n = + 2; and for the ( , 3) problem, n = 3 -1 if is odd and n = 3 -2 if is even. Then, we study the general case ( A ,D) and obtain that an upper bound on n is approximately 3(2D+1)( -2)bD/2c,
and another one is C( - 2)bD/2c if D and C is a sufficiently large constant.
Our upper bounds improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on n for maximal planar bipartite graphs, which is approximately ( - 2)k if D = 2k, and 3( - 3)k if D = 2k + 1, for and D sufficiently large in both cases.2014-09-18T10:55:22ZColored spanning graphs for set visualization
http://hdl.handle.net/2117/23314
Title: Colored spanning graphs for set visualization
Authors: Hurtado Díaz, Fernando Alfredo; Korman Cozzetti, Matias; Van Kreveld, Matias; Löffler, Maarten; Sacristán Adinolfi, Vera; Silveira, Rodrigo Ignacio; Speckmann, Bettina
Abstract: We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the blue set, red
points belong exclusively to the red set, and purple points belong to both sets.
A red-blue-purple spanning graph (RBP spanning graph) is a set of edges connecting the points such that the subgraph induced by the red and purple points is connected, and the subgraph induced by the blue and purple points is connected.
We study the geometric properties of minimum RBP spanning graphs and the algorithmic problems associated with computing them. Specifically, we show that the general problem is NP-hard. Hence we give an (1/2¿+1)-approximation, where ¿ is the Steiner ratio. We also present efficient exact solutions if the points are located on a line or a circle. Finally we consider extensions to more than two sets.2014-06-26T17:02:39ZAn open-source toolbox for motion analysis of closed-chain mechanisms
http://hdl.handle.net/2117/23201
Title: An open-source toolbox for motion analysis of closed-chain mechanisms
Authors: Porta Pleite, Josep Maria; Ros Giralt, Lluís; Bohigas Nadal, Oriol; Manubens Ferriol, Montserrat; Rosales Gallegos, Carlos; Jaillet, Leonard Georges
Abstract: Many situations in Robotics require an effective analysis of the motions of a closed-chain mechanism. Despite appearing very often in practice (e.g. in parallel manipulators, reconfigurable robots, or molecular compounds), there is a lack of general tools to effectively analyze the complex configuration spaces of such systems. This paper describes the CUIK suite, an open-source toolbox for motion analysis of general closed-chain mechanisms. The package can determine the motion range of the whole mechanism or of some of its parts, detect singular configurations leading to control or dexterity issues, or find collision- and singularity-free paths between given configurations. The toolbox is the result of several years of research and development within the Kinematics and Robot Design group at IRI, Barcelona, and is available under GPLv3 license from http://www.iri.upc.edu/cuik.2014-06-11T15:57:37ZStabbing simplices of point sets with k-flats
http://hdl.handle.net/2117/22736
Title: Stabbing simplices of point sets with k-flats
Authors: Cano, Javier; Hurtado Díaz, Fernando Alfredo; Urrutia Galicia, Jorge
Abstract: Let S be a set of n points inRdin general position.A set H of k-flats is called an mk-stabber of S if the relative interior of anym-simplex with vertices in S is intersected by at least one element of H. In thispaper we give lower and upper bounds on the size of mínimum mk-stabbers of point sets in Rd. We study mainly mk-stabbers in the plane and in R32014-04-28T16:17:42ZWitness bar visibility graphs
http://hdl.handle.net/2117/22337
Title: Witness bar visibility graphs
Authors: Cortés, Carmen; Hurtado Díaz, Fernando Alfredo; Márquez, Alberto; Valenzuela, Jesús
Abstract: Bar visibility graphs were introduced in the seventies as a model for some VLSI layout problems.
They have been also studied since then by the graph drawing community, and recently several
generalizations and restricted versions have been proposed.
We introduce a generalization, witness-bar visibility graphs, and we prove that this class encom-
passes all the bar-visibility variations considered so far. In addition, we show that many classes of graphs are contained in this family, including in particular all planar graphs, interval graphs, circular arc graphs and permutation graphs2014-03-21T16:03:37ZStabbing Segments with Rectilinear Objects
http://hdl.handle.net/2117/21700
Title: Stabbing Segments with Rectilinear Objects
Authors: Claverol Aguas, Mercè; Seara Ojea, Carlos; Garijo, Delia; Korman, M.; Silveira, Rodrigo Ignacio
Abstract: Given a set of n line segments in the plane, we say that a region R of the plane is a stabber if R contains exactly one end point of each segment of the set. In this paper we provide efficient algorithms for determining wheter or not a stabber exists for several shapes of stabbers. Specially, we consider the case in which the stabber can be described as the intersecction of isothetic halfplanes (thus the stabbers are halfplanes, strips, quadrants, 3-sided rectangles, or rectangles). We provided efficient algorithms reporting all combinatorially different stabbers of the shape. The algorithms run in O(n) time (for the halfplane case), O(n logn) time (for strips and quadrants), O(n^2) (for 3-sided rectangles), or O(n^3) time (for rectangles).2014-02-21T17:24:50ZThe alternating path problem revisited
http://hdl.handle.net/2117/21369
Title: The alternating path problem revisited
Authors: Claverol Aguas, Mercè; Garijo, Delia; Hurtado Díaz, Fernando Alfredo; Lara Cuevas, María Dolores; Seara Ojea, Carlos
Abstract: It is well known that, given "n" red points and "n" blue points on acircle, it is not always possible to find a plane geometric. Hamiltonian alternating path. In this work we prove that if we relax the constraint on the path from being plane to being 1-plane, then the problem always has a solution, and even a Hamiltonian alternating cycle can be obtained on all instances. we also extend this kind of result to other configurations and provide remarks on similar problems.2014-01-27T11:06:21ZNew results on stabbing segments with a polygon
http://hdl.handle.net/2117/20930
Title: New results on stabbing segments with a polygon
Authors: Díaz Bañez, José Miguel; Korman Cozzetti, Matías; Pérez Lantero, Pablo; Pilz, Alexander; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio
Abstract: We consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon P if at least one of its two endpoints is contained in P. A segment set S is stabbed by P if every segment of S is stabbed by P. We show that if S is a set of pairwise disjoint segments, the problem of computing the minimum perimeter polygon stabbing S can be solved in polynomial time. We also prove that for general segments the problem is NP-hard. Further, an adaptation of our polynomial-time algorithm solves an open problem posed by Löffler and van Kreveld [Algorithmica 56(2), 236-269 (2010)] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments.2013-12-05T14:38:36ZMotion planning for 6D manipulation with aerial towed-cable systems
http://hdl.handle.net/2117/20414
Title: Motion planning for 6D manipulation with aerial towed-cable systems
Authors: Manubens Ferriol, Montserrat; Devaurs, Didier; Ros Giralt, Lluís; Cortés, Juan
Abstract: Performing aerial 6-dimensional manipulation using flying robots is a challenging problem, to which only little work has been devoted. This paper proposes a motion planning approach for the reliable 6-dimensional quasi-static manipulation with an aerial towed-cable system. The novelty of this approach lies in the use of a cost-based motion-planning algorithm together
with some results deriving from the static analysis of cable-driven manipulators. Based on the so-called wrench-feasibility
constraints applied to the cable tensions, as well as thrust constraints applied to the flying robots, we formally characterize
the set of feasible configurations of the system. Besides, the expression of these constraints leads to a criterion to evaluate
the quality of a configuration. This allows us to define a cost function over the configuration space, which we exploit to
compute good-quality paths using the T-RRT algorithm. As part of our approach, we also propose an aerial towed-cable system that we name the FlyCrane. It consists of a platform
attached to three flying robots using six fixed-length cables. We validate the proposed approach on two simulated 6-D quasi-static manipulation problems involving such a system, and show the benefit of taking the cost function into account for such motion
planning tasks.2013-10-18T09:26:46ZUniversal point subsets for planar graphs
http://hdl.handle.net/2117/18077
Title: Universal point subsets for planar graphs
Authors: Angelini, Patrizio; Binucci, Carla; Evans, William; Hurtado Díaz, Fernando Alfredo; Liotta, Giuseppe; Mchedlidze, Tamara; Meijer, Henk; Okamoto, Yoshio
Abstract: A set S of k points in the plane is a universal point subset for a class G of planar graphs if every graph belonging to G admits a planar straight-line drawing such that k of its vertices are represented by the points of S . In this paper we study the following main problem: For a given class of graphs, what is the maximum k such that there exists a universal point subset of size k ? We provide a ⌈ √ n ⌉ lower bound on k for the class of planar graphs with n ver- tices. In addition, we consider the value F ( n; G ) such that every set of F ( n; G ) points in general position is a universal subset for all graphs with n vertices be- longing to the family G , and we establish upper and lower bounds for F ( n; G ) for different families of planar graphs, including 4-connected planar graphs and nested-triangles graphs.2013-03-05T17:31:44ZNumerical computation of manipulator singularities
http://hdl.handle.net/2117/17988
Title: Numerical computation of manipulator singularities
Authors: Bohigas Nadal, Oriol; Zlatanov, Dimiter; Ros Giralt, Lluís; Manubens Ferriol, Montserrat; Porta Pleite, Josep Maria
Abstract: This paper provides a method to compute all types
of singularities of non-redundant manipulators with non-helical
lower pairs and designated instantaneous input and output
speeds. A system of equations describing each singularity type is
given. Using a numerical method based on linear relaxations,
the configurations in each type are computed independently.
The method is general and complete: it can be applied to
manipulators with arbitrary geometry; and will isolate singu-
larities with the desired accuracy. As an example, the entire
singularity set and its complete classification are computed for
a two-degree-of-freedom mechanism. The complex partition of
the configuration space by various singularities is illustrated by
three-dimensional projections.2013-02-26T17:48:15ZA unified method for computing position and orientation workspaces of general Stewart platforms
http://hdl.handle.net/2117/17966
Title: A unified method for computing position and orientation workspaces of general Stewart platforms
Authors: Bohigas Nadal, Oriol; Ros, LLuís; Manubens Ferriol, Montserrat
Abstract: The workspace of a Stewart platform is a complex six-
dimensional volume embedded in the Cartesian space defined b
y
six pose parameters. Because of its large dimension and com-
plex shape, such workspace is difficult to compute and repres
ent,
so that comprehension on its structure is being gained by stu
dy-
ing its three-dimensional slices. While successful method
s have
been given to determine the constant-orientation slice, th
e com-
putation and appropriate visualization of the constant-po
sition
slice (also known as the orientation workspace) has proved t
o
be a challenging task. This paper presents a unified method fo
r
computing both of such slices, and any other ones defined by
fixing three pose parameters, on general Stewart platforms i
n-
volving mechanical limits on the active and passive joints.
Ad-
ditional advantages over previous methods include the abil
ity to
determine all connected components of the workspace, and an
y
motion barriers present in its interior.2013-02-25T19:09:18ZNavigating the wrench-feasible C-space of cable-driven hexapods
http://hdl.handle.net/2117/17457
Title: Navigating the wrench-feasible C-space of cable-driven hexapods
Authors: Bohigas Nadal, Oriol; Manubens Ferriol, Montserrat; Ros Giralt, Lluís
Abstract: Motion paths of cable-driven hexapods must carefully be planned to ensure that the lengths and tensions of all cables remain within acceptable limits, for a given wrench applied to the platform. The cables cannot go slack –to keep the control of the platform– nor excessively tight –to prevent cable breakage– even in the presence of bounded perturbations of the wrench. This paper proposes a path planning method that accommodates such constraints simultaneously. Given two configurations of the platform, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying inside a predefined uncertainty region. The resulting C-space is placed in correspondence with a smooth manifold, which allows defining a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path non-existence is proved by exhaustion of the search. The approach is illustrated on the NIST Robocrane hexapod, but it remains applicable to general cable-driven hexapods, either to navigate their full six-dimensional C-space, or any of its slices.2013-01-21T18:08:43ZPlanning singularity-free force-feasible paths on the Stewart platform
http://hdl.handle.net/2117/17355
Title: Planning singularity-free force-feasible paths on the Stewart platform
Authors: Bohigas Nadal, Oriol; Manubens Ferriol, Montserrat; Ros Giralt, Lluís
Abstract: This paper provides a method for computing force-feasible paths on the Stewart platform. Given two configurations of the platform, the method attempts to connect them through a path that, at any point, allows the platform to counteract any external wrench lying inside a predefined six-dimensional region. In particular, the Jacobian matrix of the manipulator will be full rank along such path, so that the path will not traverse the forward singularity locus at any point. The path is computed by first characterizing the force-feasible C-space of the manipulator as the solution set of a system of equations, and then using a higher-dimensional continuation technique to explore this set systematically from one configuration, until the second configuration is found. Examples are included that demonstrate the performance of the method on illustrative situations.2013-01-14T17:43:09Z