INTRODUCTION: Brief History. Multifingered Hands and Dextrous Manipulation. Outline of the Book. Bibliography. RIGID BODY MOTION: Rigid Body Transformations. Rotational Motion in R3. Rigid Motion in R3. Velocity of a Rigid Body. Wrenches and Reciprocal Screws. MANIPULATOR KINEMATICS: Introduction. Forward Kinematics. Inverse Kinematics. The Manipulator Jacobian. Redundant and Parallel Manipulators. ROBOT DYNAMICS AND CONTROL: Introduction. Lagrange's Equations. Dynamics of Open-Chain Manipulators. Lyapunov Stability Theory. Position Control and Trajectory Tracking. Control of Constrained Manipulators. MULTIFINGERED HAND KINEMATICS: Introduction to Grasping. Grasp Statics. Force-Closure. Grasp Planning. Grasp Constraints. Rolling Contact Kinematics. HAND DYNAMICS AND CONTROL: Lagrange's Equations with Constraints. Robot Hand Dynamics. Redundant and Nonmanipulable Robot Systems. Kinematics and Statics of Tendon Actuation. Control of Robot Hands. NONHOLONOMIC BEHAVIOR IN ROBOTIC SYSTEMS: Introduction. Controllability and Frobenius' Theorem. Examples of Nonholonomic Systems. Structure of Nonholonomic Systems. NONHOLONOMIC MOTION PLANNING: Introduction. Steering Model Control Systems Using Sinusoids. General Methods for Steering. Dynamic Finger Repositioning. FUTURE PROSPECTS: Robots in Hazardous Environments. Medical Applications for Multifingered Hands. Robots on a Small Scale: Microrobotics. APPENDICES: Lie Groups and Robot Kinematics. A Mathematica Package for Screw Calculus. Bibliography. Index Each chapter also includes a Summary, Bibliography, and Exercises

http://www.cds.caltech.edu/%7Emurray/books/MLS/pdf/mls94-complete.pdf

A Mathematical Introduction to Robotic Manipulation

From the Publisher:
A comprehensive treatment of model-based fuzzy control systems
This volume offers full coverage of the systematic framework for the stability and design of nonlinear fuzzy control systems. Building on the Takagi-Sugeno fuzzy model, authors Tanaka and Wang address a number of important issues in fuzzy control systems, including stability analysis, systematic design procedures, incorporation of performance specifications, numerical implementations, and practical applications.
Issues that have not been fully treated in existing texts, such as stability analysis, systematic design, and performance analysis, are crucial to the validity and applicability of fuzzy control methodology. Fuzzy Control Systems Design and Analysis addresses these issues in the framework of parallel distributed compensation, a controller structure devised in accordance with the fuzzy model.
This balanced treatment features an overview of fuzzy control, modeling, and stability analysis, as well as a section on the use of linear matrix inequalities (LMI) as an approach to fuzzy design and control. It also covers advanced topics in model-based fuzzy control systems, including modeling and control of chaotic systems. Later sections offer practical examples in the form of detailed theoretical and experimental studies of fuzzy control in robotic systems and a discussion of future directions in the field.
Fuzzy Control Systems Design and Analysis offers an advanced treatment of fuzzy control that makes a useful reference for researchers and a reliable text for advanced graduate students in the field.

Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach

Preface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Sard's Theorem.- 7 Lie Groups.- 8 Vector Fields.- 9 Integral Curves and Flows.- 10 Vector Bundles.- 11 The Cotangent Bundle.- 12 Tensors.- 13 Riemannian Metrics.- 14 Differential Forms.- 15 Orientations.- 16 Integration on Manifolds.- 17 De Rham Cohomology.- 18 The de Rham Theorem.- 19 Distributions and Foliations.- 20 The Exponential Map.- 21 Quotient Manifolds.- 22 Symplectic Manifolds.- Appendix A: Review of Topology.- Appendix B: Review of Linear Algebra.- Appendix C: Review of Calculus.- Appendix D: Review of Differential Equations.- References.- Notation Index.- Subject Index

http://ndl.ethernet.edu.et/bitstream/123456789/88506/1/2012_Book_IntroductionToSmoothManifolds.pdf

Introduction to Smooth Manifolds

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.

http://www-math.mit.edu/~edelman/publications/geometry_of_algorithms.pdf

The Geometry of Algorithms with Orthogonality Constraints

In practice the relevant details of images exist only over a restricted range of scale. Hence it is important to study the dependence of image structure on the level of resolution. It seems clear enough that visual perception treats images on several levels of resolution simultaneously and that this fact must be important for the study of perception. However, no applicable mathematically formulated theory to deal with such problems appears to exist. In this paper it is shown that any image can be embedded in a one-parameter family of derived images (with resolution as the parameter) in essentially only one unique way if the constraint that no spurious detail should be generated when the resolution is diminished, is applied. The structure of this family is governed by the well known diffusion equation (a parabolic, linear, partial differential equation of the second order). As such the structure fits into existing theories that treat the front end of the visual system as a continuous stack of homogeneous layers, characterized by iterated local processing schemes. When resolution is decreased the images becomes less articulated because the extrem ("light and dark blobs") disappear one after the other. This erosion of structure is a simple process that is similar in every case. As a result any image can be described as a juxtaposed and nested set of light and dark blobs, wherein each blob has a limited range of resolution in which it manifests itself. The structure of the family of derived images permits a derivation of the sampling density required to sample the image at multiple scales of resolution.(ABSTRACT TRUNCATED AT 250 WORDS)

/pdf/the-structure-of-images-gx3bm3792l.pdf

The structure of images

Spivak's Comprehensive introduction takes as its theme the classical roots of contemporary differential geometry. Spivak explains his Main Premise (my term) as follows: "in order for an introduction to differential geometry to expose the geometric aspect of the subject, an historical approach is necessary; there is no point in introducing the curvature tensor without explaining how it was invented and what it has to do with curvature". His second premise concerns the manner in which the historical material should be presented: "it is absurdly inefficient to eschew the modern language of manifolds, bundles, forms, etc., which was developed precisely in order to rigorize the concepts of classical differential geometry". Here, Spivak is addressing "a dilemma which confronts anyone intent on penetrating the mysteries of differential geometry". On the one hand, the subject is an old one, dating, as we know it, from the works of Gauss and Riemann, and possessing a rich classical literature. On the other hand, the rigorous and systematic formulations in current use were established relatively recently, after topological techniques had been sufficiently well developed to provide a base for an abstract global theory; the coordinate-free geometric methods of E. Cartan were also a major source. Furthermore, the viewpoint of global structure theory now dominates the subject, whereas differential geometers were traditionally more concerned with the local study of geometric objects. Thus it is possible and not uncommon for a modern geometric education to leave the subject's classical origins obscure. Such an approach can offer the great advantages of elegance, efficiency, and direct access to the most active areas of modern research. At the same time, it may strike the student as being frustratingly incomplete. As Spivak remarks, "ignorance of the roots of the subject has its price-no one denies that modern formulations are clear, elegant and precise; it's just that it's impossible to comprehend how any one ever thought of them." While Spivak's impulse to mediate between the past and the present is a natural one and is by no means unique, his undertaking is remarkable for its ambitious scope. Acting on its second premise, the Comprehensive introduction opens with an introduction to differentiable manifolds; the remaining four volumes are devoted to a geometric odyssey which starts with Gauss and Riemann, and ends with the Gauss-Bonnet-Chern Theorem and characteristic classes. A formidable assortment of topics is included along the way, in which we may distinguish several major historical themes: In the first place, the origins of fundamental geometric concepts are investigated carefully. As just one example, Riemannian sectional curvature is introduced by a translation and close exposition of the text of Riemann's remarkable paper, Über die Hypothesen, welche der Geometrie zu Grunde

A comprehensive introduction to differential geometry

Functions on Euclidean Space * Norm and inner Product * Subsets of Euclidean Space * Functions and Continuity Differentiation * Basic Definitions * Basic Theorems * Partial Derivatives * Inverse Functions * Implicit Functions * Notation Integration * Basic Definitions * Measure Zero and Content Zero * Integrable Functions * Fubinis Theorem * Partitions of Unity * Change of Variable Integration on Chains * Algebraic Preliminaries * Fields and Forms * Geometric Preliminaries * The Fundamental Theorem of Calculus Integration on Manifolds * Manifolds * Fields and Forms on Manifolds * Stokes Theorem on Manifolds * The Volume Element * The Classical Theorems

Calculus on Manifolds

On spaces satisfying Poincare duality

Spaces satisfying Poincaré duality

This is the second edition of The Joy of TEX, the user-friendly guide to AMS-TEX, which is a software package based on the revolutionary computer typesetting language TEX. AMS-TEX was designed to simplify the typesetting of mathematical quantitites, equations, and displays, and to format the output according to any of various preset style specifications. This manual is useful for technical typists as well as scientists who prepare their own manuscripts.

Michael David Spivak

Papers

A comprehensive introduction to differential geometry

Calculus on Manifolds

On spaces satisfying Poincare duality

Spaces satisfying Poincaré duality

The joy of TEX : a gourmet guide to typesetting with the AMS-TEX macro package