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A Tutorial on Visual Servo Control
 IEEE Transactions on Robotics and Automation
, 1996
"... This paper provides a tutorial introduction to visual servo control of robotic manipulators. Since the topic spans many disciplines our goal is limited to providing a basic conceptual framework. We begin by reviewing the prerequisite topics from robotics and computer vision, including a brief review ..."
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Cited by 822 (25 self)
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This paper provides a tutorial introduction to visual servo control of robotic manipulators. Since the topic spans many disciplines our goal is limited to providing a basic conceptual framework. We begin by reviewing the prerequisite topics from robotics and computer vision, including a brief review of coordinate transformations, velocity representation, and a description of the geometric aspects of the image formation process. We then present a taxonomy of visual servo control systems. The two major classes of systems, positionbased and imagebased systems, are then discussed. Since any visual servo system must be capable of tracking image features in a sequence of images, we include an overview of featurebased and correlationbased methods for tracking. We conclude the tutorial with a number of observations on the current directions of the research field of visual servo control. 1 Introduction Today there are over 800,000 robots in the world, mostly working in factory environment...
The geometry of algorithms with orthogonality constraints
 SIAM J. MATRIX ANAL. APPL
, 1998
"... In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal proces ..."
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Cited by 649 (1 self)
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In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms. The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view of previously unrelated algorithms. It is our hope that developers of new algorithms and perturbation theories will benefit from the theory, methods, and examples in this paper.
RungeKutta methods on Lie groups
, 1997
"... . We construct generalized Runge#Kutta methods for integration of di#erential equations evolving on a Lie group. The methods are using intrinsic operations on the group, and we are hence guaranteed that the numerical solution will evolveonthe correct manifold. Our methods must satisfy two di#erent ..."
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Cited by 86 (17 self)
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. We construct generalized Runge#Kutta methods for integration of di#erential equations evolving on a Lie group. The methods are using intrinsic operations on the group, and we are hence guaranteed that the numerical solution will evolveonthe correct manifold. Our methods must satisfy two di#erent criteria to achieve a given order: # Coe#cients A i;j and b j must satisfy the classical order conditions. This is done by picking the coe#cients of any classical RK scheme of the given order. # Wemust construct functions to correct for certain non#commutative e#ects to the given order. These tasks are completely independent, so once correction functions are found to the given order, we can turn any classical RK scheme into a RK method of the same order on any Lie group. The theory in this paper shows the tight connections between the algebraic structure of the order conditions of RK methods and the algebraic structure of the so called `universal enveloping algebra' of Lie algebras. This m...
CutandPaste Editing of Multiresolution Surfaces
, 2002
"... Cutting and pasting to combine different elements into a common structure are widely used operations that have been successfully adapted to many media types. Surface design could also benefit from the availability of a general, robust, and efficient cutandpaste tool, especially during the initial s ..."
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Cited by 78 (5 self)
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Cutting and pasting to combine different elements into a common structure are widely used operations that have been successfully adapted to many media types. Surface design could also benefit from the availability of a general, robust, and efficient cutandpaste tool, especially during the initial stages of design when a large space of alternatives needs to be explored. Techniques to support cutandpaste operations for surfaces have been proposed in the past, but have been of limited usefulness due to constraints on the type of shapes supported and the lack of realtime interaction. In this paper, we describe a set of algorithms based on multiresolution subdivision surfaces that perform at interactive rates and enable intuitive cutandpaste operations.
Introductory lectures on contact geometry
"... Though contact topology was born over two centuries ago, in the work of Huygens, Hamilton and Jacobi on geometric optics, and been studied by many great mathematicians, such as Sophus Lie, Elie Cartan and Darboux, it has only recently moved into the foreground of mathematics. The last decade has wit ..."
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Cited by 61 (7 self)
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Though contact topology was born over two centuries ago, in the work of Huygens, Hamilton and Jacobi on geometric optics, and been studied by many great mathematicians, such as Sophus Lie, Elie Cartan and Darboux, it has only recently moved into the foreground of mathematics. The last decade has witnessed many remarkable breakthroughs in contact topology, resulting in
A new sixdimensional irreducible symplectic variety
 J. Alg. Geom
"... 1. Introduction. There are three types of “building blocks ” in the Bogomolov decomposition [B, Th.2] of compact Kählerian manifolds with torsion c1, namely complex tori, CalabiYau varieties, and irreducible symplectic manifolds. We are interested in the last type, i.e. simplyconnected compact Käh ..."
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Cited by 60 (2 self)
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1. Introduction. There are three types of “building blocks ” in the Bogomolov decomposition [B, Th.2] of compact Kählerian manifolds with torsion c1, namely complex tori, CalabiYau varieties, and irreducible symplectic manifolds. We are interested in the last type, i.e. simplyconnected compact Kählerian manifolds carrying a holomorphic
Wave equations on Lorentzian manifolds and quantization
, 2007
"... In General Relativity spacetime is described mathematically by a Lorentzian manifold. Gravitation manifests itself as the curvature of this manifold. Physical fields, such as the electromagnetic field, are defined on this manifold and have to satisfy a wave equation. This book provides an introducti ..."
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Cited by 47 (0 self)
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In General Relativity spacetime is described mathematically by a Lorentzian manifold. Gravitation manifests itself as the curvature of this manifold. Physical fields, such as the electromagnetic field, are defined on this manifold and have to satisfy a wave equation. This book provides an introduction to the theory of linear wave equations on Lorentzian manifolds. In contrast to other texts on this topic [Friedlander1975, Günther1988] we develop the global theory. This means, we ask for existence and uniqueness of solutions which are defined on all of the underlying manifold. Such results are of great importance and are already used much in the literature despite the fact that published proofs are missing. Tracing back the references one typically ends at Leray’s unpublished lecture notes [Leray1953] or their exposition [ChoquetBruhat1968]. In this text we develop the global theory from scratch in a modern geometric language. In the first chapter we provide basic definitions and facts about distributions on manifolds, Lorentzian geometry, and normally hyperbolic operators. We study the building blocks for local solutions, the Riesz distributions, in some detail. In the second chapter we show how to solve wave equations locally. Using Riesz distributions and a formal recursive procedure
Lectures on analytic differential equations
 Graduate Studies in Mathematics
, 2008
"... The book combines the features of a graduatelevel textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes selfcontained, sometimes considerably simplified dem ..."
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Cited by 45 (2 self)
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The book combines the features of a graduatelevel textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes selfcontained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the RiemannHilbert problem, EcalleVoronin and MartinetRamis moduli, solution of the Poincaré problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the more recent results surveyed in the text.
Geometric quantization and the generalized Segal–Bargmann transform for Lie groups of compact type
, 2001
"... Let K be a connected Lie group of compact type and let T ∗ (K) be its cotangent bundle. This paper considers geometric quantization of T ∗ (K), first using the vertical polarization and then using a natural Kähler polarization obtained by identifying T ∗ (K) with the complexified group KC. The firs ..."
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Cited by 42 (11 self)
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Let K be a connected Lie group of compact type and let T ∗ (K) be its cotangent bundle. This paper considers geometric quantization of T ∗ (K), first using the vertical polarization and then using a natural Kähler polarization obtained by identifying T ∗ (K) with the complexified group KC. The first main result is that the Hilbert space obtained by using the Kähler polarization is naturally identifiable with the generalized Segal–Bargmann space introduced by the author from a different point of view, namely that of heat kernels. The second main result is that the pairing map of geometric quantization coincides with the generalized Segal–Bargmann transform introduced by the author. This means that in this case the pairing map is a constant multiple of a unitary map. For both results it is essential that the halfform correction be included when using the Kähler polarization. These results should be understood in the context of results of K. Wren and of the author with B. Driver concerning the quantization of 1+1dimensional Yang–Mills theory. Together with those results the present paper may be seen as an instance of “quantization commuting with reduction.”