Topology And Robotics
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Topology And Robotics
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Author : Michael Farber
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Topology And Robotics written by Michael Farber and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Ever since the literary works of Capek and Asimov, mankind has been fascinated by the idea of robots. Modern research in robotics reveals that along with many other branches of mathematics, topology has a fundamental role to play in making these grand ideas a reality. This volume summarizes recent progress in the field of topological robotics--a new discipline at the crossroads of topology, engineering and computer science. Currently, topological robotics is developing in two main directions. On one hand, it studies pure topological problems inspired by robotics and engineering. On the other hand, it uses topological ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of engineering and computer science. Examples of research in both these directions are given by articles in this volume, which is designed to be a mixture of various interesting topics of pure mathematics and practical engineering.
Invitation To Topological Robotics
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Author : Michael Farber
language : en
Publisher: European Mathematical Society
Release Date : 2008
Invitation To Topological Robotics written by Michael Farber and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book discusses several selected topics of a new emerging area of research on the interface between topology and engineering. The first main topic is topology of configuration spaces of mechanical linkages. These manifolds arise in various fields of mathematics and in other sciences, e.g., engineering, statistics, molecular biology. To compute Betti numbers of these configuration spaces the author applies a new technique of Morse theory in the presence of an involution. A significant result of topology of linkages presented in this book is a solution of a conjecture of Kevin Walker which states that the relative sizes of bars of a linkage are determined, up to certain equivalence, by the cohomology algebra of the linkage configuration space. This book also describes a new probabilistic approach to topology of linkages which treats the bar lengths as random variables and studies mathematical expectations of Betti numbers. The second main topic is topology of configuration spaces associated to polyhedra. The author gives an account of a beautiful work of S. R. Gal, suggesting an explicit formula for the generating function encoding Euler characteristics of these spaces. Next the author studies the knot theory of a robot arm, focusing on a recent important result of R. Connelly, E. Demain, and G. Rote. Finally, he investigates topological problems arising in the theory of robot motion planning algorithms and studies the homotopy invariant TC(X) measuring navigational complexity of configuration spaces. This book is intended as an appetizer and will introduce the reader to many fascinating topological problems motivated by engineering.
Modern Robotics
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Author : Kevin M. Lynch
language : en
Publisher: Cambridge University Press
Release Date : 2017-05-25
Modern Robotics written by Kevin M. Lynch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-25 with Computers categories.
A modern and unified treatment of the mechanics, planning, and control of robots, suitable for a first course in robotics.
Topology And Its Applications
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Author : William F. Basener
language : en
Publisher: John Wiley & Sons
Release Date : 2006-11-03
Topology And Its Applications written by William F. Basener and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-03 with Mathematics categories.
Discover a unique and modern treatment of topology employing a cross-disciplinary approach Implemented recently to understand diverse topics, such as cell biology, superconductors, and robot motion, topology has been transformed from a theoretical field that highlights mathematical theory to a subject that plays a growing role in nearly all fields of scientific investigation. Moving from the concrete to the abstract, Topology and Its Applications displays both the beauty and utility of topology, first presenting the essentials of topology followed by its emerging role within the new frontiers in research. Filling a gap between the teaching of topology and its modern uses in real-world phenomena, Topology and Its Applications is organized around the mathematical theory of topology, a framework of rigorous theorems, and clear, elegant proofs. This book is the first of its kind to present applications in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, and population modeling, as well as other areas of science and engineering. Many of these applications are presented in optional sections, allowing an instructor to customize the presentation. The author presents a diversity of topological areas, including point-set topology, geometric topology, differential topology, and algebraic/combinatorial topology. Topics within these areas include: Open sets Compactness Homotopy Surface classification Index theory on surfaces Manifolds and complexes Topological groups The fundamental group and homology Special "core intuition" segments throughout the book briefly explain the basic intuition essential to understanding several topics. A generous number of figures and examples, many of which come from applications such as liquid crystals, space probe data, and computer graphics, are all available from the publisher's Web site.
Topology Unravelling The Fabric Of Space
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-04-20
Topology Unravelling The Fabric Of Space written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-20 with Mathematics categories.
Embark on a captivating journey through the world of topology with Topology: Unravelling the Fabric of Space, a comprehensive guide that unveils the intricate beauty and profound insights of this fascinating mathematical discipline. Discover how topology unravels the fabric of space, providing a framework for understanding the structure of our universe and beyond. Delve into the fundamental concepts of topology, exploring the properties of geometric figures that remain unchanged under continuous deformations. Uncover the significance of topological spaces, homeomorphisms, and homology, and witness how these concepts lay the foundation for understanding the structure and behavior of shapes and spaces. Explore the realm of topological invariants, numerical measures that capture the essence of geometric objects. Learn how these invariants enable mathematicians to classify and compare different shapes and spaces, providing deep insights into their underlying structure. Discover the applications of topological invariants in diverse fields, from physics and engineering to computer science and biology. Witness the power of topology in unraveling the mysteries of the physical world. Delve into the geometry of spacetime, the fundamental fabric of our universe, and understand how topology provides insights into the behavior of elementary particles, the structure of atoms, and the properties of black holes. Discover the profound impact of topology on computer science, where it finds applications in computer graphics, image processing, and network analysis. Explore how topological algorithms efficiently represent and manipulate complex data structures, optimize routing protocols, and design efficient algorithms for solving computational problems. Topology: Unravelling the Fabric of Space is an indispensable resource for students, researchers, and anyone fascinated by the intricate world of shapes and spaces. Its comprehensive coverage of fundamental concepts, theorems, and applications makes it an invaluable guide to the captivating realm of topology. If you like this book, write a review on google books!
Algorithmic Foundations Of Robotics Viii
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Author : Gregory S. Chirikjian
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-04
Algorithmic Foundations Of Robotics Viii written by Gregory S. Chirikjian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-04 with Technology & Engineering categories.
This book contains selected contributions to WAFR, the highly-competitive meeting on the algorithmic foundations of robotics. They address the unique combination of questions that the design and analysis of robot algorithms inspires.
Topology For Computing
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Author : Afra J. Zomorodian
language : en
Publisher: Cambridge University Press
Release Date : 2005-01-10
Topology For Computing written by Afra J. Zomorodian and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-10 with Computers categories.
The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.
Geometry Topology And Mathematical Physics
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Author : V. M. Buchstaber
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Geometry Topology And Mathematical Physics written by V. M. Buchstaber and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
The second half of the 20th century and its conclusion : crisis in the physics and mathematics community in Russia and in the West -- Interview with Sergey P. Novikov -- The w-function of the KdV hierarchy -- On the zeta functions of a meromorphic germ in two variables -- On almost duality for Frobenius manifolds -- Finitely presented semigroups in knot theory. Oriented case -- Topological robotics : subspace arrangements and collision free motion planning -- The initial-boundary value problem on the interval for the nonlinear Schrödinger equation. The algebro-geometric approach. I -- On odd Laplace operators. II -- From 2D Toda hierarchy to conformal maps for domains of the Riemann sphere --Integrable chains on algebraic curves -- Fifteen years of KAM for PDE -- Graded filiform Lie algebras and symplectic nilmanifolds --Adiabatic limit in the Seiberg-Witten equations -- Affine Krichever-Novikov algebras, their representations and applications -- Tame integrals of motion and o-minimal structures.
Topology Design Of Robot Mechanisms
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Author : Ting-Li Yang
language : en
Publisher: Springer
Release Date : 2018-01-02
Topology Design Of Robot Mechanisms written by Ting-Li Yang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-02 with Technology & Engineering categories.
This book focuses on the topology theory of mechanisms developed by the authors and provides a systematic method for the topology design of robot mechanisms. The main original theoretical contributions of this book include: A. Three basic concepts · The “geometrical constraint type of axes” is introduced as the third element of the topological structure of a mechanism. When it is combined with the other two elements, the kinematic pair and the connection of links, the symbolic expression of the topological structure is independent of the motion positions (except for the singularity positions) and the fixed coordinate system (Chapter 2). · The position and orientation characteristic (POC) set is used to describe the POC of the relative motion between any two links. The POC set, derived from the unit vector set of the velocity of a link, is only depend on the topological structure of a mechanism. Therefore, it is also independent of the motion positions and the fixed coordinate system (Chapter 3). · The single open chain (SOC) unit is the base unit of the topological structure used to develop the four basic equations of the mechanism topology (Chapters 2, 4–6). B. The mechanism composition principle based on the SOC units This book proposes a mechanism composition principle, based on the SOC units, to establish a systematic theory for the unified modeling of the topology, kinematics, and dynamics of mechanisms based on the SOC units (Chapter 7). C. Four basic equations • The POC equation of serial mechanisms with 10 symbolic operation rules (Chapter 4). • The POC equation of parallel mechanisms with 14 symbolic operation rules (Chapter 5). • The general DOF formula for spatial mechanisms (Chapter 6). • The coupling degree formula for the Assur kinematic chain (Chapter 7). D. One systematic method for the topology design of robot mechanisms (Chapters 8–10) Based on the three basic concepts and the four basic equations addressed above, this book puts forward a systematic method for the topology design of parallel mechanisms, which is fundamentally different from all existing methods. Its main characteristics are as follows: • The design process includes two stages: the first is structure synthesis, which derives many structure types; the second involves the performance analysis, classification and optimization of structure types derived from the first stage. • The design operation is independent of the motion positions and the fixed coordinate system. Therefore, the proposed method is essentially a geometrical method, which ensures the full-cycle DOF and the generality of geometric conditions of mechanism existence. • Each individual design step follows an explicit formula or the guidelines for design criteria, making the operation simple, feasible and reproducible. In addition, the topology design of the SCARA PMs is studied in detail to demonstrate the proposed method (Chapter 10).
Robotics Research
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Author : Paolo Dario
language : en
Publisher: Springer
Release Date : 2005-08-24
Robotics Research written by Paolo Dario and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-24 with Technology & Engineering categories.
ISRR, the "International Symposium on Robotics Research", is one of robotics’ pioneering symposia, which has established some of the field's most fundamental and lasting contributions over the past two decades. This book presents the results of the eleventh edition of "Robotics Research" ISRR03, offering a broad range of topics in robotics. The contributions provide a wide coverage of the current state of robotics research: the advances and challenges in its theoretical foundation and technology basis, and the developments in its traditional and new emerging areas of applications. The diversity, novelty, and span of the work unfolding in these areas reveal the field's increased maturity and expanded scope, and define the state of the art of robotics and its future direction.