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233
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 593 (19 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 383 (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.
The Convenient Setting of Global Analysis
, 1997
"... ichor i Table of Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 CHAPTER I Calculus of Smooth Mappings . . . . . . . . . . . . . . . . . . . . 4 1. Smooth Curves . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1a. Completeness . . . . . . . . . . . . . . ..."
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Cited by 198 (47 self)
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ichor i Table of Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 CHAPTER I Calculus of Smooth Mappings . . . . . . . . . . . . . . . . . . . . 4 1. Smooth Curves . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1a. Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1b. Smooth Mappings and the Exponential Law . . . . . . . . . . . . . 17 2. The c 1 Topology . . . . . . . . . . . . . . . . . . . . . . . . . 29 3. Uniform Boundedness Principles and Multilinearity . . . . . . . . . . 47 3a. Some Spaces of Smooth Functions . . . . . . . . . . . . . . . . . 59 Historical remarks on the development of smooth calculus . . . . . . . . . 63 CHAPTER II Partitions of Unity . . . . . . . . . . . . . . . . . . . . . . . . . 68 5. D
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 71 (14 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 67 (7 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 44 (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
Bounds on packings of spheres in the Grassmann manifolds
, 2000
"... We derive the VarshamovGilbert and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over $\mathbb R$ and $\mathbb C$. The distance between two $k$planes is defined as $\rho(p,q)=(\sin^2\theta_1 \dots \sin^2\theta_k)^{1/2}$, where $\theta_i, 1\le i\le k$, are the principal ..."
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Cited by 29 (1 self)
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We derive the VarshamovGilbert and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over $\mathbb R$ and $\mathbb C$. The distance between two $k$planes is defined as $\rho(p,q)=(\sin^2\theta_1 \dots \sin^2\theta_k)^{1/2}$, where $\theta_i, 1\le i\le k$, are the principal angles between $p$ and $q$.
Approximation by Quantum Circuits
 and 68Q9529 at http://www.c3.lanl.gov/laces, Los Alamos National Laboratory
, 1995
"... In a recent preprint by Deutsch et al. [5] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on n qubits by 2qubit unitary operations. We address that comment by proving strong lower bounds on the approximation capabilities of gqubit unitary operati ..."
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Cited by 28 (4 self)
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In a recent preprint by Deutsch et al. [5] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on n qubits by 2qubit unitary operations. We address that comment by proving strong lower bounds on the approximation capabilities of gqubit unitary operations for fixed g. We consider approximation of unitary operations on subspaces as well as approximation of states and of density matrices by quantum circuits in several natural metrics. The ability of quantum circuits to probabilistically solve decision problem and guess checkable functions is discussed. We also address exact unitary representation by reducing the upper bound by a factor of n 2 and by formalizing the argument given by Barenco et al. [1] for the lower bound. The overall conclusion is that almost all problems are hard to solve with quantum circuits. 1 Introduction There has recently been great interest in the properties of quantum computation and quantum circuits, partly due...
Flux Invariants for Shape
 In CVPR
, 2003
"... We consider the average outward flux through a Jordan curve of the gradient vector field of the Euclidean distance function to the boundary of a 2D shape. Using an alternate form of the divergence theorem, we show that in the limit as the area of the region enclosed by such a curve shrinks to zero, ..."
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Cited by 28 (3 self)
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We consider the average outward flux through a Jordan curve of the gradient vector field of the Euclidean distance function to the boundary of a 2D shape. Using an alternate form of the divergence theorem, we show that in the limit as the area of the region enclosed by such a curve shrinks to zero, this measure has very different behaviours at medial points than at nonmedial ones, providing a theoretical justification for its use in the HamiltonJacobi skeletonization algorithm of [7]. We then specialize to the case of shrinking circular neighborhoods and show that the average outward flux measure also reveals the object angle at skeletal points. Hence, formulae for obtaining the boundary curves, their curvatures, and other geometric quantities of interest, can be written in terms of the average outward flux limit values at skeletal points. Thus this measure can be viewed as a Euclidean invariant for shape description: it can be used to both detect the skeleton from the Euclidean distance function, as well as to explicitly reconstruct the boundary from it. We illustrate our results with several numerical simulations. 1.
Nonlinear Control of Mechanical Systems: A Riemannian Geometry Approach
, 1998
"... Nonlinear control of mechanical systems is a challenging discipline that lies at the intersection between control theory and geometric mechanics. This thesis sheds new light on this interplay while investigating motion control problems for Lagrangian systems. Both stability and motion planning aspec ..."
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Cited by 24 (0 self)
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Nonlinear control of mechanical systems is a challenging discipline that lies at the intersection between control theory and geometric mechanics. This thesis sheds new light on this interplay while investigating motion control problems for Lagrangian systems. Both stability and motion planning aspects are treated within a unified framework that accounts for a large class of devices such as robotic manipulators, autonomous vehicles and locomotion systems. One distinguishing feature of mechanical systems is the number of control forces. For systems with as many input forces as degrees of freedom, many control problems are tractable. One contribution of this thesis is a set of trajectory tracking controllers designed via the notions of configuration and velocity error. The proposed approach includes as special cases a variety of results on joint and workspace control of manipulators as well as on attitude and position control of vehicles. Whenever fewer input forces are available than deg...