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Maria Alberich-Carramiñana

Publications and source records attributed to Maria Alberich-Carramiñana.

At least 19 recordsLinked to original sources
arXiv2026

A Simple Gripper Interface for Simulator-Agnostic Cloth Manipulation

This paper presents a grasping model for cloth manipulation specifically tailored to ease the deployment of robotic control methods. The model is robust, fast and easy to implement avoiding at the same time contact and friction considerations between the gripper and the cloth in favor of simple positional constraints. The gripper is described by its pose, jaw state, and an attached grasping volume. Two kinds of grasping volumes are considered: an axis-aligned box to simulate a pinch grasping and a square pyramidal volume to simulate point grasping. When the gripper closes, the discrete cloth positions lying inside this volume are selected, stored in the local gripper frame, and then transported with the gripper motion. A simple squeezing step is also included to progressively move the selected cloth positions toward the center of the grasping region, avoiding an instantaneous displacement at closure. The model can be used in any simulator as it only requires access to discrete cloth positions and a mechanism for imposing target positions as constraints. We implement our grasping model in conjunction with a constraint-based inextensible cloth simulator, where grasping is implemented as moving positional equality constraints coupled with stretch, shear, collision, and table contact projection steps. The same gripper trajectory is applied on a robot arm to fold a real piece of cloth, serving as a simple bridge between simulation and physical cloth manipulation and showcasing the realism and practicality of our idealized grasping model.

cs.RO↗
arXiv2024

Topological reconstruction of sampled surfaces via Morse theory

In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as those obtained with 3D scanners. We present a reconstruction algorithm based on a careful topological study of the point sample that allows us to obtain a cellular decomposition of it using a Morse function. No triangulation or local implicit equations are used as intermediate steps, avoiding in this way reconstruction-induced artifices. The algorithm can be run without any prior knowledge of the surface topology, density or regularity of the point-sample. The results consist of a piece-wise decomposition of the given surface as a union of Morse cells (i.e. topological disks), suitable for tasks such as mesh-independent reparametrization or noise-filtering, and a small-rank cellular complex determining the topology of the surface. The algorithm, which we test with several real and synthetic surfaces, can be applied to smooth surfaces with or without boundary, embedded in an ambient space of any dimension.

cs.CG↗
arXiv2024

Limit distribution of Hodge spectral exponents of irreducible plane curve singularities

We study the distribution of the Hodge spectral exponents of an irreducible plane curve by comparing it with a continuous distribution. We provide a closed formula for this difference in terms of numerical invariants of the curve. We characterize those families of irreducible plane curves whose limit distribution of Hodge spectral exponents is the continuous distribution and we provide intervals of dominating values.

math.AG↗
arXiv2023

A novel collision model for inextensible textiles and its experimental validation

In this work, we introduce a collision model specifically tailored for the simulation of inextensible textiles. The model considers friction, contacts, and inextensibility constraints all at the same time without any decoupling. Self-collisions are modeled in a natural way that allows considering the thickness of cloth without introducing unwanted oscillations. The discretization of the equations of motion leads naturally to a sequence of quadratic problems with inequality and equality constraints. In order to solve these problems efficiently, we develop a novel active-set algorithm that takes into account past active constraints to accelerate the resolution of unresolved contacts. We put to a test the developed collision procedure with diverse scenarios involving static and dynamic friction, sharp objects, and complex-topology folding sequences. Finally, we perform an experimental validation of the collision model by comparing simulations with recordings of real textiles as given by a $\textit{Motion Capture System}$. The results are very accurate, having errors around 1 cm for DIN A2 textiles (42 x 59.4 cm) even in difficult scenarios involving fast and strong hits with a rigid object.

cs.RO↗
arXiv2023

Okutsu frames of irreducible polynomials over henselian fields

For a henselian valued field $(K,v)$ we establish a complete parallelism between the arithmetic properties of irreducible polynomials $F\in K[x]$, encoded by their Okutsu frames, and the valuation-theoretic properties of their induced valuations $v_F$ on $K[x]$, encoded by their MacLane-Vaquié chains. This parallelism was only known for defectless irreducible polynomials.

math.AC↗
arXiv2022

Curve singularities with one Puiseux pair and value sets of modules over their local rings

In this paper we characterize the value set $Δ$ of the $R$-modules of the form $R+zR$ for the local ring $R$ associated to a germ $ξ$ of an irreducible plane curve singularity with one Puiseux pair. In the particular case of the module of Kähler differentials attached to $ξ$, we recover some results of Delorme. From our characterization of $Δ$ we introduce a proper subset of semimodules over the value semigroup of the ring $R$. Moreover, we provide a geometric algorithm to construct all possible semimodules in this subset for a given value semigroup.

math.AC↗
arXiv2022

The dGLI Cloth Coordinates: A Topological Representation for Semantic Classification of Cloth States

Robotic manipulation of cloth is a highly complex task because of its infinite-dimensional shape-state space that makes cloth state estimation very difficult. In this paper we introduce the dGLI Cloth Coordinates, a low-dimensional representation of the state of a rectangular piece of cloth that allows to efficiently distinguish key topological changes in a folding sequence, opening the door to efficient learning methods for cloth manipulation planning and control. Our representation is based on a directional derivative of the Gauss Linking Integral and allows us to represent both planar and spatial configurations in a consistent unified way. The proposed dGLI Cloth Coordinates are shown to be more accurate in the classification of cloth states and significantly more sensitive to changes in grasping affordances than other classic shape distance methods. Finally, we apply our representation to real images of a cloth, showing we can identify the different states using a simple distance-based classifier.

cs.RO↗
arXiv2022

Polynomial factorization over henselian fields

Given a valued field $(K,v)$ and an irreducible polynomial $g\in K[x]$, we survey the ideas of Ore, Maclane, Okutsu, Montes, Vaquié and Herrera-Olalla-Mahboub-Spivakovsky, leading (under certain conditions) to an algorithm to find the factorization of $g$ over a henselization of $(K,v)$.

math.AC↗
arXiv2022

Valuative trees over valued fields

For an arbitrary valued field $(K,v)$ and a given extension $v(K^*)\hookrightarrowΛ$ of ordered groups, we analyze the structure of the tree formed by all $Λ$-valued extensions of $v$ to the polynomial ring $K[x]$. As an application, we find a model for the tree of all equivalence classes of valuations on $K[x]$ (without fixing their value group), whose restriction to $K$ is equivalent to $v$. In the henselian case, we apply these results to show that there is a complete parallelism between the arithmetic properties of irreducible polynomials $F\in K[x]$, encoded by their Okutsu frames, and the valuation-theoretic properties of their induced valuations $v_F$ on $K[x]$, encoded by their MacLane-Vaquié chains. This parallelism was only known for defectless irreducible polynomials.

math.AG↗
arXiv2022

Valuations with infinite limit-depth

For a certain field $K$, we construct a valuation-algebraic valuation on the polynomial ring $K[x]$, whose Maclane--Vaquié chain consists of an infinite (countable) number of limit augmentations

math.AC↗
arXiv2021

An Inextensible Model for Robotic Simulations of Textiles

We introduce a new isometric strain model for the study of the dynamics of cloth garments in a moderate stress environment, such as robotic manipulation in the neighborhood of humans. This model treats textiles as surfaces which are inextensible, admitting only isometric motions. Inextensibility is imposed in a continuous setting, prior to any discretization, which gives consistency with respect to re-meshing and prevents the problem of locking even with coarse meshes. The simulations of robotic manipulation using the model are compared to the actual manipulation in the real world, finding that the error between the simulated and real position of each point in the garment is lower than 1cm in average, even when a coarse mesh is used. Aerodynamic contributions to motion are incorporated to the model through the virtual uncoupling of the inertial and gravitational mass of the garment. This approach results in an accurate, as compared to reality, description of cloth motion incorporating aerodynamic effects by using only two parameters.

cs.RO↗
arXiv2021

Developable surfaces with prescribed boundary

It is proved that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. The relevance of this result in the context of the dynamics of developable surfaces is discussed.

math.DG↗
arXiv2020

Invariants of limit key polynomials

Let $ν$ be a valuation of arbitrary rank on the polynomial ring $K[x]$ with coefficients in a field $K$. We prove comparison theorems between MacLane-Vaquié key polynomials for valuations $μ\leν$ and abstract key polynomials for $ν$. Also, some results on invariants attached to limit key polynomials are obtained. In particular, if $\operatorname{char}(K)=0$ we show that all limit key polynomials of unbounded continuous MacLane chains have numerical character equal to one.

math.AG↗
arXiv2020

The minimal Tjurina number of irreducible germs of plane curve singularities

In this paper we give a positive answer to a question of Dimca and Greuel about the quotient between the Milnor and the Tjurina numbers for any irreducible germ of plane curve singularity. This result is based on a closed formula for the minimal Tjurina number of an equisingularity class in terms of the sequence of multiplicities of the strict transform along a resolution. The key points for the proof are previous results by Genzmer, Wall and Mattei.

math.AG↗
arXiv2019

Quadratic Planar Differential Systems with Algebraic Limit Cycles via Quadratic Plane Cremona Maps

In this paper we show how we can transform quadratic systems into new quadratic systems after some kind of birational transformations, the quadratic plane Cremona maps. We afterwards apply these transformations to the families of quadratic differential systems having an algebraic limit cycle. As a consequence, we provide a new family of quadratic systems having an algebraic limit cycle of degree 5. Moreover we show how the known families of quadratic differential systems having an algebraic limit cycle of degree greater than four are obtained using these transformations. We also provide the phase portraits on the Poincaré disk of all the families of quadratic differential systems having algebraic limit cycles.

math.DS↗
arXiv2018

Multiplicities of jumping points for mixed multiplier ideals

In this paper we make a systematic study of the multiplicity of the jumping points associated to the mixed multiplier ideals of a family of ideals in a complex surface with rational singularities. In particular we study the behaviour of the multiplicity by small perturbations of the jumping points. We also introduce a Poincaré series for mixed multiplier ideals and prove its rationality. Finally, we study the set of divisors that contribute to the log-canonical wall.

math.AG↗
arXiv2017

Monomial generators of complete planar ideals

We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the minimal log-resolution of the ideal. Furthermore, the monomial expression given by our method is an equisingularity invariant of the ideal. As an outcome, we provide a geometric method to compute the integral closure of a planar ideal and we apply our algorithm to some families of complete ideals.

math.AG↗