43 research outputs found

    Evolution Of Special Ruled Surfaces Via The Evolution Of Their Directrices In Euclidean 3-Space E3

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    In this paper, evolutions of ruled surfaces that are generated by the normal and binormal vector fields of space curve (normal and binormal surfaces) are presented. These evolutions of the ruled surfaces depend on the evolutions of their directrices. Geometric visualization of these ruled surfaces are presented. In addition, the conditions which make these surfaces of types inextensible, developable and minimal are obtained

    Inextensible flows of curves in the equiform geometry of the pseudo-Galilean space G13

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    In this paper, we study inextensible flows of curves in 3-dimensional pseudoGalilean space. We give necessary and sufficient conditions for inextensible flows of curves according to equiform geometry in pseudo-Galilean space.Publisher's Versio

    Robotic manipulation of cloth: mechanical modeling and perception

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    (Eng) In this work we study various mathematical problems arising from the robotic manipulation of cloth. First, we develop a locking-free continuous model for the physical simulation of inextensible textiles. We present a novel 'finite element' discretization of our inextensibility constraints which results in a unified treatment of triangle and quadrilateral meshings of the cloth. Next, we explain how to incorporate contacts, self-collisions and friction into the equations of motion, so that frictional forces and inextensibility and collision constraints may be integrated implicitly and without any decoupling. We develop an efficient 'active-set' solver tailored to our non-linear problem which takes into account past active constraints to accelerate the resolution of unresolved contacts and moreover can be initialized from any non-necessarily feasible point. Then, we embark ourselves in the empirical validation of the developed model. We record in a laboratory setting --with depth cameras and motion capture systems-- the motions of seven types of textiles (including e.g. cotton, denim and polyester) of various sizes and at different speeds and end up with more than 80 recordings. The scenarios considered are all dynamic and involve rapid shaking and twisting of the textiles, collisions with frictional objects and even strong hits with a long stick. We then, compare the recorded textiles with the simulations given by our inextensible model, and find that on average the mean error is of the order of 1 cm even for the largest sizes (DIN A2) and the most challenging scenarios. Furthermore, we also tackle other problems relevant to robotic cloth manipulation, such as cloth perception and classification of its states. We present a reconstruction algorithm based on Morse theory that proceeds directly from a point-cloud to obtain a cellular decomposition of a surface with or without boundary: the results are a piecewise parametrization of the cloth surface as a union of Morse cells. From the cellular decomposition the topology of the surface can be then deduced immediately. Finally, we study the configuration space of a piece of cloth: since the original state of a piece of cloth is flat, the set of possible states under the inextensible assumption is the set of developable surfaces isometric to a fixed one. We prove that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. Inspired on this result we introduce the dGLI cloth coordinates, a low-dimensional representation of the state of a piece of cloth based on a directional derivative of the Gauss Linking Integral. These coordinates --computed from the position of the cloth's boundary-- allow to distinguish key qualitative changes in folding sequences.(Esp) En este trabajo estudiamos varios problemas matem谩ticos relacionados con la manipulaci贸n rob贸tica de textiles. En primer lugar, desarrollamos un modelo continuo libre de 'locking' para la simulaci贸n f铆sica de textiles inextensibles. Presentamos una novedosa discretizaci贸n usando 'elementos finitos' de nuestras restricciones de inextensibilidad resultando en un tratamiento unificado de mallados triangulares y cuadrangulares de la tela. A continuaci贸n, explicamos c贸mo incorporar contactos, autocolisiones y fricci贸n en las ecuaciones de movimiento, de modo que las fuerzas de fricci贸n y las restricciones de inextensibilidad y colisiones puedan integrarse impl铆citamente y sin ning煤n desacoplamiento. Desarrollamos un 'solver' de tipo 'conjunto-activo' adaptado a nuestro problema no lineal que tiene en cuenta las restricciones activas pasadas para acelerar la resoluci贸n de los contactos no resueltos y, adem谩s, puede inicializarse desde cualquier punto no necesariamente factible. Posteriormente, nos embarcamos en la validaci贸n emp铆rica del modelo desarrollado. Grabamos en un entorno de laboratorio -con c谩maras de profundidad y sistemas de captura de movimiento- los movimientos de siete tipos de textiles (entre los que se incluyen, por ejemplo, algod贸n, tela vaquera y poli茅ster) de varios tama帽os y a diferentes velocidades, terminando con m谩s de 80 grabaciones. Los escenarios considerados son todos din谩micos e implican sacudidas y torsiones r谩pidas de los textiles, colisiones con obst谩culos e incluso golpes con una varilla cil铆ndrica. Finalmente, comparamos las grabaciones con las simulaciones dadas por nuestro modelo inextensible, y encontramos que, de media, el error es del orden de 1 cm incluso para las telas m谩s grandes (DIN A2) y los escenarios m谩s complicados. Adem谩s, tambi茅n abordamos otros problemas relevantes para la manipulaci贸n rob贸tica de telas, como son la percepci贸n y la clasificaci贸n de sus estados. Presentamos un algoritmo de reconstrucci贸n basado en la teor铆a de Morse que procede directamente de una nube de puntos para obtener una descomposici贸n celular de una superficie con o sin borde: los resultados son una parametrizaci贸n a trozos de la superficie de la tela como una uni贸n de celdas de Morse. A partir de la descomposici贸n celular puede deducirse inmediatamente la topolog铆a de la superficie. Por 煤ltimo, estudiamos el espacio de configuraci贸n de un trozo de tela: dado que el estado original de la tela es plano, el conjunto de estados posibles bajo la hip贸tesis de inextensibilidad es el conjunto de superficies desarrollables isom茅tricas a una fija. Demostramos que una curva gen茅rica simple, cerrada y regular a trozos en el espacio puede ser el borde de un n煤mero finito de superficies desarrollables con curvatura media no nula. Inspir谩ndonos en este resultado, introducimos las coordenadas dGLI, una representaci贸n de dimensi贸n baja del estado de un pedazo de tela basada en una derivada direccional de la integral de enlazamiento de Gauss. Estas coordenadas -calculadas a partir de la posici贸n del borde de la tela- permiten distinguir cambios cualitativos clave en distintas secuencias de plegado.Postprint (published version

    Robotic manipulation of cloth: mechanical modeling and perception

    Get PDF
    (Eng) In this work we study various mathematical problems arising from the robotic manipulation of cloth. First, we develop a locking-free continuous model for the physical simulation of inextensible textiles. We present a novel 'finite element' discretization of our inextensibility constraints which results in a unified treatment of triangle and quadrilateral meshings of the cloth. Next, we explain how to incorporate contacts, self-collisions and friction into the equations of motion, so that frictional forces and inextensibility and collision constraints may be integrated implicitly and without any decoupling. We develop an efficient 'active-set' solver tailored to our non-linear problem which takes into account past active constraints to accelerate the resolution of unresolved contacts and moreover can be initialized from any non-necessarily feasible point. Then, we embark ourselves in the empirical validation of the developed model. We record in a laboratory setting --with depth cameras and motion capture systems-- the motions of seven types of textiles (including e.g. cotton, denim and polyester) of various sizes and at different speeds and end up with more than 80 recordings. The scenarios considered are all dynamic and involve rapid shaking and twisting of the textiles, collisions with frictional objects and even strong hits with a long stick. We then, compare the recorded textiles with the simulations given by our inextensible model, and find that on average the mean error is of the order of 1 cm even for the largest sizes (DIN A2) and the most challenging scenarios. Furthermore, we also tackle other problems relevant to robotic cloth manipulation, such as cloth perception and classification of its states. We present a reconstruction algorithm based on Morse theory that proceeds directly from a point-cloud to obtain a cellular decomposition of a surface with or without boundary: the results are a piecewise parametrization of the cloth surface as a union of Morse cells. From the cellular decomposition the topology of the surface can be then deduced immediately. Finally, we study the configuration space of a piece of cloth: since the original state of a piece of cloth is flat, the set of possible states under the inextensible assumption is the set of developable surfaces isometric to a fixed one. We prove that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. Inspired on this result we introduce the dGLI cloth coordinates, a low-dimensional representation of the state of a piece of cloth based on a directional derivative of the Gauss Linking Integral. These coordinates --computed from the position of the cloth's boundary-- allow to distinguish key qualitative changes in folding sequences.(Esp) En este trabajo estudiamos varios problemas matem谩ticos relacionados con la manipulaci贸n rob贸tica de textiles. En primer lugar, desarrollamos un modelo continuo libre de 'locking' para la simulaci贸n f铆sica de textiles inextensibles. Presentamos una novedosa discretizaci贸n usando 'elementos finitos' de nuestras restricciones de inextensibilidad resultando en un tratamiento unificado de mallados triangulares y cuadrangulares de la tela. A continuaci贸n, explicamos c贸mo incorporar contactos, autocolisiones y fricci贸n en las ecuaciones de movimiento, de modo que las fuerzas de fricci贸n y las restricciones de inextensibilidad y colisiones puedan integrarse impl铆citamente y sin ning煤n desacoplamiento. Desarrollamos un 'solver' de tipo 'conjunto-activo' adaptado a nuestro problema no lineal que tiene en cuenta las restricciones activas pasadas para acelerar la resoluci贸n de los contactos no resueltos y, adem谩s, puede inicializarse desde cualquier punto no necesariamente factible. Posteriormente, nos embarcamos en la validaci贸n emp铆rica del modelo desarrollado. Grabamos en un entorno de laboratorio -con c谩maras de profundidad y sistemas de captura de movimiento- los movimientos de siete tipos de textiles (entre los que se incluyen, por ejemplo, algod贸n, tela vaquera y poli茅ster) de varios tama帽os y a diferentes velocidades, terminando con m谩s de 80 grabaciones. Los escenarios considerados son todos din谩micos e implican sacudidas y torsiones r谩pidas de los textiles, colisiones con obst谩culos e incluso golpes con una varilla cil铆ndrica. Finalmente, comparamos las grabaciones con las simulaciones dadas por nuestro modelo inextensible, y encontramos que, de media, el error es del orden de 1 cm incluso para las telas m谩s grandes (DIN A2) y los escenarios m谩s complicados. Adem谩s, tambi茅n abordamos otros problemas relevantes para la manipulaci贸n rob贸tica de telas, como son la percepci贸n y la clasificaci贸n de sus estados. Presentamos un algoritmo de reconstrucci贸n basado en la teor铆a de Morse que procede directamente de una nube de puntos para obtener una descomposici贸n celular de una superficie con o sin borde: los resultados son una parametrizaci贸n a trozos de la superficie de la tela como una uni贸n de celdas de Morse. A partir de la descomposici贸n celular puede deducirse inmediatamente la topolog铆a de la superficie. Por 煤ltimo, estudiamos el espacio de configuraci贸n de un trozo de tela: dado que el estado original de la tela es plano, el conjunto de estados posibles bajo la hip贸tesis de inextensibilidad es el conjunto de superficies desarrollables isom茅tricas a una fija. Demostramos que una curva gen茅rica simple, cerrada y regular a trozos en el espacio puede ser el borde de un n煤mero finito de superficies desarrollables con curvatura media no nula. Inspir谩ndonos en este resultado, introducimos las coordenadas dGLI, una representaci贸n de dimensi贸n baja del estado de un pedazo de tela basada en una derivada direccional de la integral de enlazamiento de Gauss. Estas coordenadas -calculadas a partir de la posici贸n del borde de la tela- permiten distinguir cambios cualitativos clave en distintas secuencias de plegado

    Whirling skirts and rotating cones

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    Steady, dihedrally symmetric patterns with sharp peaks may be observed on a spinning skirt, lagging behind the material flow of the fabric. These qualitative features are captured with a minimal model of traveling waves on an inextensible, flexible, generalized-conical sheet rotating about a fixed axis. Conservation laws are used to reduce the dynamics to a quadrature describing a particle in a three-parameter family of potentials. One parameter is associated with the stress in the sheet, aNoether is the current associated with rotational invariance, and the third is a Rossby number which indicates the relative strength of Coriolis forces. Solutions are quantized by enforcing a topology appropriate to a skirt and a particular choice of dihedral symmetry. A perturbative analysis of nearly axisymmetric cones shows that Coriolis effects are essential in establishing skirt-like solutions. Fully non-linear solutions with three-fold symmetry are presented which bear a suggestive resemblance to the observed patterns.Comment: two additional figures, changes to text throughout. journal version will have a wordier abstrac
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