Invitation To Topological Robotics
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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.
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.
Algorithmic Foundations Of Robotics Xv
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Author : Steven M. LaValle
language : en
Publisher: Springer Nature
Release Date : 2022-12-14
Algorithmic Foundations Of Robotics Xv written by Steven M. LaValle and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-14 with Technology & Engineering categories.
This book includes significant recent research on robotic algorithms. It has been written by leading experts in the field. The 15th Workshop on the Algorithmic Foundations of Robotics (WAFR) was held on June 22–24, 2022, at the University of Maryland, College Park, Maryland. Each chapter represents an exciting state-of-the-art development in robotic algorithms that was presented at this 15th incarnation of WAFR. Different chapters combine ideas from a wide variety of fields, spanning and combining planning (for tasks, paths, motion, navigation, coverage, and patrol), computational geometry and topology, control theory, machine learning, formal methods, game theory, information theory, and theoretical computer science. Many of these papers explore new and interesting problems and problem variants that include human–robot interaction, planning and reasoning under uncertainty, dynamic environments, distributed decision making, multi-agent coordination, and heterogeneity.
Combinatorial And Toric Homotopy Introductory Lectures
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Author : Darby Alastair
language : en
Publisher: World Scientific
Release Date : 2017-10-20
Combinatorial And Toric Homotopy Introductory Lectures written by Darby Alastair and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-20 with Mathematics categories.
This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning. The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis–Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics. The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students. Contents: Toric Homotopy Theory (Stephen Theriault)Fullerenes, Polytopes and Toric Topology (Victor M Buchstaber and Nikolay Yu Erokhovets)Around Braids (Vladimir Vershinin)Higher Limits, Homology Theories and fr-Codes (Sergei O Ivanov and Roman Mikhailov)Configuration Spaces and Robot Motion Planning Algorithms (Michael Farber)Cellular Stratified Spaces (Dai Tamaki) Readership: Advanced undergraduate and graduate students as well as researchers interested in homotopy theory and its applications in the sciences. Keywords: Toric Topology;Toric Homotopy;Configuration Space;Stratified Spaces;Braid Group;Fullerene;Polytope;Virtual Braid Group;Thompson Group;Robotics;Motion PlanningReview: Key Features: The first book in the area of toric homotopy theory consisting of introductory lectures on the topics and their applications to fr-codes and robot motion planning
Algorithmic Foundations Of Robotics Xi
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Author : H. Levent Akin
language : en
Publisher: Springer
Release Date : 2015-04-30
Algorithmic Foundations Of Robotics Xi written by H. Levent Akin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-30 with Technology & Engineering categories.
This carefully edited volume is the outcome of the eleventh edition of the Workshop on Algorithmic Foundations of Robotics (WAFR), which is the premier venue showcasing cutting edge research in algorithmic robotics. The eleventh WAFR, which was held August 3-5, 2014 at Boğaziçi University in Istanbul, Turkey continued this tradition. This volume contains extended versions of the 42 papers presented at WAFR. These contributions highlight the cutting edge research in classical robotics problems (e.g. manipulation, motion, path, multi-robot and kinodynamic planning), geometric and topological computation in robotics as well novel applications such as informative path planning, active sensing and surgical planning. This book - rich by topics and authoritative contributors - is a unique reference on the current developments and new directions in the field of algorithmic foundations.
Topological Complexity And Related Topics
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Author : Mark Grant
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-02-14
Topological Complexity And Related Topics written by Mark Grant 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 2018-02-14 with Algebraic topology categories.
This volume contains the proceedings of the mini-workshop on Topological Complexity and Related Topics, held from February 28–March 5, 2016, at the Mathematisches Forschungsinstitut Oberwolfach. Topological complexity is a numerical homotopy invariant, defined by Farber in the early twenty-first century as part of a topological approach to the motion planning problem in robotics. It continues to be the subject of intensive research by homotopy theorists, partly due to its potential applicability, and partly due to its close relationship to more classical invariants, such as the Lusternik–Schnirelmann category and the Schwarz genus. This volume contains survey articles and original research papers on topological complexity and its many generalizations and variants, to give a snapshot of contemporary research on this exciting topic at the interface of pure mathematics and engineering.
An Invitation To Morse Theory
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Author : Liviu Nicolaescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-02
An Invitation To Morse Theory written by Liviu Nicolaescu 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 2011-12-02 with Mathematics categories.
This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.
Advances In Applied And Computational Topology
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Author : American Mathematical Society. Short Course on Computational Topology
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-07-05
Advances In Applied And Computational Topology written by American Mathematical Society. Short Course on Computational Topology 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 2012-07-05 with Mathematics categories.
What is the shape of data? How do we describe flows? Can we count by integrating? How do we plan with uncertainty? What is the most compact representation? These questions, while unrelated, become similar when recast into a computational setting. Our input is a set of finite, discrete, noisy samples that describes an abstract space. Our goal is to compute qualitative features of the unknown space. It turns out that topology is sufficiently tolerant to provide us with robust tools. This volume is based on lectures delivered at the 2011 AMS Short Course on Computational Topology, held January 4-5, 2011 in New Orleans, Louisiana. The aim of the volume is to provide a broad introduction to recent techniques from applied and computational topology. Afra Zomorodian focuses on topological data analysis via efficient construction of combinatorial structures and recent theories of persistence. Marian Mrozek analyzes asymptotic behavior of dynamical systems via efficient computation of cubical homology. Justin Curry, Robert Ghrist, and Michael Robinson present Euler Calculus, an integral calculus based on the Euler characteristic, and apply it to sensor and network data aggregation. Michael Erdmann explores the relationship of topology, planning, and probability with the strategy complex. Jeff Erickson surveys algorithms and hardness results for topological optimization problems.
Progress In Industrial Mathematics At Ecmi 2008
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Author : Alistair D. Fitt
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-23
Progress In Industrial Mathematics At Ecmi 2008 written by Alistair D. Fitt 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 2010-07-23 with Mathematics categories.
The 15th European Conference on Mathematics for Industry was held in the agreeable surroundings of University College London, just 5 minutes walk from the British Museum in the heart of London, over the ?ve warm, sunny days from 30 June to 4 July 2008. Participants from all over the world met with the commonaimofreinforcingthe roleofmathematics asanoverarching resource for industry and business. The conference attracted over 300 participants from 30 countries, most of them participating with either a contributed talk, a minisymposium pres- tation or a plenary lecture. ‘Mathematics in Industry’ was interpreted in its widest sense as can be seen from the range of applications and techniques described in this volume. We mention just two examples. The Alan Tayler Lecture was given by Mario Primicerio on a problem arising from moving oil through pipelines when temperature variations a?ect the shearing properties of wax and thus modify the ?ow. The Wacker Prize winner, Master’s student Lauri Harhanen from the Helsinki University of Technology, showed how a novel piece of mathematics allowed new software to capture real-time images of teeth from the data supplied by present day dental machinery (see ECMI Newsletter 44). The meeting was attended by leading ?gures from government, bu- ness and science who all shared the same aim – to promote the application of innovative mathematics to industry, and identify industrial sectors that o?er the most exciting opportunities for mathematicians to provide new insight and new ideas.
The Mathematics Of Data
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Author : Michael W. Mahoney
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-11-15
The Mathematics Of Data written by Michael W. Mahoney 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 2018-11-15 with Big data categories.
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