274 research outputs found
Rapid learning of humanoid body schemas with kinematic Bezier maps
Trabajo presentado al 9th IEEE-RAS celebrado en París del 7 al 10 de diciembre de 2009.This paper addresses the problem of hand-eye coordination and, more specifically, tool-eye recalibration of humanoid robots. Inspired by results from neuroscience, a novel method to learn the forward kinematics model as part of the body schema of humanoid robots is presented. By making extensive use of techniques borrowed from the field of computer-aided geometry, the proposed Kinematic Be ́zier Maps (KB-Maps) permit reducing this complex problem to a linearly-solvable, although high-dimensional, one. Therefore, in the absence of noise, an exact kinematic model is obtained. This leads to rapid learning which, unlike in other approaches, is combined with good extrapolation capabilities. These promising theoretical advantages have been validated through simulation, and the applicability of the method to real hardware has been demonstrated through experiments on the humanoid robot ARMAR-IIIa.This work was supported by projects: 'Perception, action & cognition through learning of object-action complexes.' (4915), 'Analysis and motion planning of complex robotic systems' (4802), 'Grup de recerca consolidat - Grup de Robòtica' (4810). The work described in this paper was partially conducted within the EU Cognitive Systems projects GRASP (FP7-215821) and PACO-PLUS (FP6-027657) funded by the European Commission.
The authors acknowledge support from the Generalitat de Catalunya under the consolidated Robotics group, and from the Spanish Ministry of
Science and Education, under the project DPI2007-60858Peer Reviewe
Methods for constraint-based conceptual free-form surface design
Zusammenfassung
Der constraint-basierte Entwurf von Freiformfl„chen ist eine m„chtige Methode im
Computer gest�tzten Entwurf. Bekannte Realisierungen beschr„nken sich jedoch meist
auf Interpolation von Rand- und isoparametrischen Kurven. In diesem Zusammenhang
sind die sog. "Multi-patch" Methoden die am weitesten verbreitete Vorgehensweise. Hier
versucht man Fl„chenverb„nde aus einem Netz von dreidimensionalen Kurven (oft
gemischt mit unstrukturierten Punktewolken) derart zu generieren, dass die Kurven und
Punkte von den Fl„chen interpoliert werden. Die Kurven werden als R„nder von
rechteckigen oder dreieckigen bi-polynomialen oder polynomialen Fl„chen betrachtet.
Unter dieser Einschr„nkung leidet die Flexibilit„t des Verfahrens. In dieser Dissertation
schlagen wir vor, beliebige, d.h. auch nicht iso-parametrische, Kurven zu verwenden.
Dadurch ergeben sich folgende Vorteile: Erstens kann so beispielsweise eine B-spline
Fl„che entlang einer benutzerdefinierten Kurve verformt werden w„hrend andere Kurven
oder Punkte fixiert sind. Zweitens, kann eine B-spline Fl„che Kurven interpolieren, die sich
nicht auf iso-parametrische Linien der Fl„che abbilden lassen. Wir behandeln drei Arten
von Constraints: Inzidenz einer beliebigen Kurve auf einer B-spline Fl„che, Fixieren von
Fl„chennormalen entlang einer beliebigen Kurve (dieser Constraint dient zur Herstellung
von tangentialen šberg„ngen zwischen zwei Fl„chen) und die sog. Variational
Constrains. Letztere dienen unter anderem zur Optimierung der physikalischen und
optischen Eigenschaften der Fl„chen. Es handelt sich hierbei um die Gausschen
Normalgleichungen der Fl„chenfunktionale zweiter Ordnung, wie sie in der Literatur
bekannt sind.
Die Dissertation gliedert sich in zwei Teile. Der erste Teil befasst sich mit der Aufstellung
der linearen Gleichungssysteme, welche die oben erw„hnten Constraints repr„sentieren.
Der zweite Teil behandelt Methoden zum L”sen dieser Gleichungssysteme. Der Kern des
ersten Teiles ist die Erweiterung und Generalisierung des auf Polarformen (Blossoms)
basierenden Algorithmus f�r Verkettung von Polynomen auf Bezier und B-spline Basis:
Gegeben sei eine B-spline Fl„che und eine B-spline Kurve im Parameterraum der Fl„che.
Wir zeigen, dass die Kontrollpunkte der dreidimensionalen Fl„chenkurve, welche als
polynomiale Verkettung der beiden definiert ist, durch eine im Voraus berechenbare
lineare Tranformation (eine Matrix) der Fl„chenkontrollpunkte ausgedr�ckt werden
k”nnen. Dadurch k”nnen Inzidenzbeziehungen zwischen Kurven und Fl„chen exakt und
auf eine sehr elegante und kompakte Art definiert werden. Im Vergleich zu den bekannten
Methoden ist diese Vorgehensweise effizienter, numerisch stabiler und erh”ht nicht die
Konditionszahl der zu l”senden linearen Gleichungen. Die Effizienz wird erreicht durch
Verwendung von eigens daf�r entwickelten Datenstrukturen und sorgf„ltige Analyse von
kombinatorischen Eigenschaften von Polarformen. Die Gleichungen zur Definition von
Tangentialit„ts- und Variational Constraints werden als Anwendung und Erweiterung
dieses Algorithmus implementiert. Beschrieben werden auch symbolische und
numerische Operationen auf B-spline Polynomen (Multiplikation, Differenzierung,
Integration). Dabei wird konsistent die Matrixdarstellung von B-spline Polynomen
verwendet.
Das L”sen dieser Art von Constraintproblemen bedeutet das Finden der Kontrollpunkte
einer B-spline Fl„che derart, dass die definierten Bedingungen erf�llt werden. Dies wird
durch L”sen von, im Allgemeinen, unterbestimmten und schlecht konditionierten linearen
Gleichungssystemen bewerkstelligt. Da in solchen F„llen keine eindeutige, numerisch
stabile L”sung existiert, f�hren die �blichen Methoden zum L”sen von linearen
Gleichungssystemen nicht zum Erfolg. Wir greifen auf die Anwendung von sog.
Regularisierungsmethoden zur�ck, die auf der Singul„rwertzerlegung (SVD) der
Systemmatrix beruhen. Insbesondere wird die L-curve eingesetzt, ein "numerischer
Hochfrequenzfilter", der uns in die Lage versetzt eine stabile L”sung zu berechnen.
Allerdings reichen auch diese Methoden im Allgemeinen nicht aus, eine Fl„che zu
generieren, welche die erw�nschten „sthetischen und physikalischen Eigenschaften
besitzt. Verformt man eine Tensorproduktfl„che entlang einer nicht isoparametrischen
Kurve, entstehen unerw�nschte Oszillationen und Verformungen. Dieser Effekt wird
"Surface-Aliasing" genannt. Wir stellen zwei Methoden vor um diese Aliasing-Effekte zu
beseitigen: Die erste Methode wird vorzugsweise f�r Deformationen einer existierenden
B-spline Fl„che entlang einer nicht isoparametrischen Kurve angewendet. Es erfogt eine
Umparametrisierung der zu verformenden Fl„che derart, dass die Kurve in der neuen
Fl„che auf eine isoparametrische Linie abgebildet wird. Die Umparametrisierung einer B-
spline Fl„che ist keine abgeschlossene Operation; die resultierende Fl„che besitzt i.A.
keine B-spline Darstellung. Wir berechnen eine beliebig genaue Approximation der
resultierenden Fl„che mittels Interpolation von Kurvennetzen, die von der
umzuparametrisierenden Fl„che gewonnen werden. Die zweite Methode ist rein
algebraisch: Es werden zus„tzliche Bedingungen an die L”sung des Gleichungssystems
gestellt, die die Aliasing-Effekte unterdr�cken oder ganz beseitigen. Es wird ein
restriktionsgebundenes Minimum einer Zielfunktion gesucht, deren globales Minimum bei
"optimaler" Form der Fl„che eingenommen wird. Als Zielfunktionen werden
Gl„ttungsfunktionale zweiter Ordnung eingesetzt. Die stabile L”sung eines solchen
Optimierungsproblems kann aufgrund der nahezu linearen Abh„ngigkeit des Gleichungen
nur mit Hilfe von Regularisierungsmethoden gewonnen werden, welche die vorgegebene
Zielfunktion ber�cksichtigen. Wir wenden die sog. Modifizierte Singul„rwertzerlegung in
Verbindung mit dem L-curve Filter an. Dieser Algorithmus minimiert den Fehler f�r die
geometrischen Constraints so, dass die L”sung gleichzeitig m”glichst nah dem Optimum
der Zielfunktion ist.The constrained-based design of free-form surfaces is currently limited to tensor-product
interpolation of orthogonal curve networks or equally spaced grids of points. The, so-
called, multi-patch methods applied mainly in the context of scattered data interpolation
construct surfaces from given boundary curves and derivatives along them. The limitation
to boundary curves or iso-parametric curves considerably lowers the flexibility of this
approach. In this thesis, we propose to compute surfaces from arbitrary (that is, not only
iso-parametric) curves. This allows us to deform a B-spline surface along an arbitrary
user-defined curve, or, to interpolate a B-spline surface through a set of curves which
cannot be mapped to iso-parametric lines of the surface. We consider three kinds of
constraints: the incidence of a curve on a B-spline surface, prescribed surface normals
along an arbitrary curve incident on a surface and the, so-called, variational constraints
which enforce a physically and optically advantageous shape of the computed surfaces.
The thesis is divided into two parts: in the first part, we describe efficient methods to set
up the equations for above mentioned linear constraints between curves and surfaces. In
the second part, we discuss methods for solving such constraints. The core of the first part
is the extension and generalization of the blossom-based polynomial composition
algorithm for B-splines: let be given a B-spline surface and a B-spline curve in the domain
of that surface. We compute a matrix which represents a linear transformation of the
surface control points such that after the transformation we obtain the control points of the
curve representing the polynomial composition of the domain curve and the surface. The
result is a 3D B-spline curve always exactly incident on the surface. This, so-called,
composition matrix represents a set of linear curve-surface incidence constraints.
Compared to methods used previously our approach is more efficient, numerically more
stable and does not unnecessarily increase the condition number of the matrix. The thesis
includes a careful analysis of the complexity and combinatorial properties of the algorithm.
We also discuss topics regarding algebraic operations on B-spline polynomials
(multiplication, differentiation, integration). The matrix representation of B-spline
polynomials is used throughout the thesis. We show that the equations for tangency and
variational constraints are easily obtained re-using the methods elaborated for incidence
constraints.
The solving of generalized curve-surface constraints means to find the control points of
the unknown surface given one or several curves incident on that surface. This is
accomplished by solving of large and, generally, under-determined and badly conditioned
linear systems of equations. In such cases, no unique and numerically stable solution
exists. Hence, the usual methods such as Gaussian elimination or QR-decomposition
cannot be applied in straightforward manner. We propose to use regularization methods
based on Singular Value Decomposition (SVD). We apply the so-called L-curve, which
can be seen as an numerical high-frequency filter. The filter automatically singles out a
stable solution such that best possible satisfaction of defined constraints is achieved.
However, even the SVD along with the L-curve filter cannot be applied blindly: it turns out
that it is not sufficient to require only algebraic stability of the solution. Tensor-product
surfaces deformed along arbitrary incident curves exhibit unwanted deformations due to
the rectangular structure of the model space. We discuss a geometric and an algebraic
method to remove this, so-called, Surface aliasing effect. The first method reparametrizes
the surface such that a general curve constraint is converted to iso-parametric curve
constraint which can be easily solved by standard linear algebra methods without aliasing.
The reparametrized surface is computed by means of the approximated surface-surface
composition algorithm, which is also introduced in this thesis. While this is not possible
symbolically, an arbitrary accurate approximation of the resulting surface is obtained using
constrained curve network interpolation. The second method states additional constraints
which suppress or completely remove the aliasing. Formally we solve a constrained least
square approximation problem: we minimize an surface objective function subject to
defined curve constraints. The objective function is chosen such that it takes in the
minimal value if the surface has optimal shape; we use a linear combination of second
order surface smoothing functionals. When solving such problems we have to deal with
nearly linearly dependent equations. Problems of this type are called ill-posed. Therefore
sophisticated numerical methods have to be applied in order to obtain a set of degrees of
freedom (control points of the surface) which are sufficient to satisfy given constraints. The
remaining unused degrees of freedom are used to enforce an optically pleasing shape of
the surface. We apply the Modified Truncated SVD (MTSVD) algorithm in connection with
the L-curve filter which determines a compromise between an optically pleasant shape of
the surface and constraint satisfaction in a particularly efficient manner
Doctor of Philosophy
dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest
Algebraic level sets for CAD/CAE integration and moving boundary problems
Boundary representation (B-rep) of CAD models obtained from solid modeling kernels are commonly used in design, and analysis applications outside the CAD systems. Boolean operations between interacting B-rep CAD models as well as analysis of such multi-body systems are fundamental operations on B-rep geometries in CAD/CAE applications. However, the boundary representation of B-rep solids is, in general, not a suitable representation for analysis operations which lead to CAD/CAE integration challenges due to the need for conversion from B-rep to volumetric approximations. The major challenges include intermediate mesh generation step, capturing CAD features and associated behavior exactly and recurring point containment queries for point classification as inside/outside the solid. Thus, an ideal analysis technique for CAD/CAE integration that can enable direct analysis operations on B-rep CAD models while overcoming the associated challenges is desirable. ^ Further, numerical surface intersection operations are typically necessary for boolean operations on B-rep geometries during the CAD and CAE phases. However, for non-linear geometries, surface intersection operations are non-trivial and face the challenge of simultaneously satisfying the three goals of accuracy, efficiency and robustness. In the class of problems involving multi-body interactions, often an implicit knowledge of the boolean operation is sufficient and explicit intersection computation may not be needed. Such implicit boolean operations can be performed by point containment queries on B-rep CAD models. However, for complex non-linear B-rep geometries, the point containment queries may involve numerical iterative point projection operations which are expensive. Thus, there is a need for inexpensive, non-iterative techniques to enable such implicit boolean operations on B-rep geometries. ^ Moreover, in analysis problems with evolving boundaries (ormoving boundary problems), interfaces or cracks, blending functions are used to enrich the underlying domain with the known behavior on the enriching entity. The blending functions are typically dependent on the distance from the evolving boundaries. For boundaries defined by free form curves or surfaces, the distance fields have to be constructed numerically. This may require either a polytope approximation to the boundary and/or an iterative solution to determine the exact distance to the boundary. ^ In this work a purely algebraic, and computationally efficient technique is described for constructing signed distance measures from Non-Uniform Rational B-Splines (NURBS) boundaries that retain the geometric exactness of the boundaries while eliminating the need for iterative and non-robust distance calculation. The proposed technique exploits the NURBS geometry and algebraic tools of implicitization. Such a signed distance measure, also referred to as the Algebraic Level Sets, gives a volumetric representation of the B-rep geometry constructed by purely non-iterative algebraic operations on the geometry. This in turn enables both the implicit boolean operations and analysis operations on B-rep geometries in CAD/CAE applications. Algebraic level sets ensure exactness of geometry while eliminating iterative numerical computations. Further, a geometry-based analysis technique that relies on hierarchical partition of unity field compositions (HPFC) theory and its extension to enriched field modeling is presented. The proposed technique enables direct analysis of complex physical problems without meshing, thus, integrating CAD and CAE. The developed techniques are demonstrated by constructing algebraic level sets for complex geometries, geometry-based analysis of B-rep CAD models and a variety of fracture examples culminating in the analysis of steady state heat conduction in a solid with arbitrary shaped three-dimensional cracks. ^ The proposed techniques are lastly applied to investigate the risk of fracture in the ultra low-k (ULK) dies due to copper (Cu) wirebonding process. Maximum damage induced in the interlayer dielectric (ILD) stack during the process steps is proposed as an indicator of the reliability risk. Numerical techniques based on enriched isogeometric approximations are adopted to model damage in the ULK stacks using a cohesive damage description. A damage analysis procedure is proposed to conduct damage accumulation studies during Cu wirebonding process. Analysis is carried out to identify weak interfaces and potential sites for crack nucleation as well as damage nucleation patterns. Further, the critical process condition is identified by analyzing the damage induced during the impact and ultrasonic excitation stages. Also, representative ILD stack designs with varying Cu percentage are compared for risk of fracture
Pseudoedge--a hierarchical skeletal modeler for the computer aided design of structural components
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1991.Includes bibliographical references (p. 121-122).by David Leo Bonner.M.S
Enhanced meshfree RPIM with NURBS basis function for analysis of irregular boundary domain
Radial Point Interpolation Method (RPIM) has become a powerful tool to numerical analysis due to its ability to provide a higher-order approximation function with the Kronecker delta property, by which the field nodes can be fitted exactly. However, one of the major drawbacks of RPIM is the inefficiency in handling irregular domain problems. This paper presents an enhanced RPIM formulation that employs Non-Uniform Rational B-Splines (NURBS) basis functions to represent the exact geometry of the boundary domain. The NURBS is a mathematical model which provides an efficient and numerically stable algorithm to exactly represent all conic sections in engineering modelling. Taking advantage of the flexibility and adaptivity of RPIM approximation and the accuracy of geometric representations by NURBS, this new method is able to improve geometry accuracy and flexibility in numerical analysis, thus providing a better and more rational approach to analyze irregular domain problems. Numerical problem of steady heat transfer considering curved beam is presented to verify the validity and accuracy of the developed method. The essential boundary condition can simply be imposed using direct imposition as in Finite Element Method (FEM). The result shows that the RPIM/NURBS achieved the converged solution much faster than conventional RPIM and FEM, with the number of nodes required only less than 200 for an error of less than 0.01%. This shows the potential of the developed method as a powerful numerical technique for future development
Computer Aided Grid Interface: An Interactive CFD Pre-Processor
NASA maintains an applications oriented computational fluid dynamics (CFD) efforts complementary to and in support of the aerodynamic-propulsion design and test activities. This is especially true at NASA/MSFC where the goal is to advance and optimize present and future liquid-fueled rocket engines. Numerical grid generation plays a significant role in the fluid flow simulations utilizing CFD. An overall goal of the current project was to develop a geometry-grid generation tool that will help engineers, scientists and CFD practitioners to analyze design problems involving complex geometries in a timely fashion. This goal is accomplished by developing the Computer Aided Grid Interface system (CAGI). The CAGI system is developed by integrating CAD/CAM (Computer Aided Design/Computer Aided Manufacturing) geometric system output and / or Initial Graphics Exchange Specification (IGES) files (including all the NASA-IGES entities), geometry manipulations and generations associated with grid constructions, and robust grid generation methodologies. This report describes the development process of the CAGI system
Efficient integration of software components for scientific simulations
Abstract unavailable please refer to PD
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