Download or read book Invitation to Topological Robotics written by Michael Farber and published by European Mathematical Society. This book was released on 2008 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topology and Robotics written by Michael Farber and published by American Mathematical Soc.. This book was released on 2007 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algorithmic Foundations of Robotics XV written by Steven M. LaValle and published by Springer Nature. This book was released on 2022-12-14 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Combinatorial And Toric Homotopy Introductory Lectures written by Alastair Darby and published by World Scientific. This book was released on 2017-10-20 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algorithmic Foundations of Robotics XI written by H. Levent Akin and published by Springer. This book was released on 2015-04-30 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topological Complexity and Related Topics written by Mark Grant and published by American Mathematical Soc.. This book was released on 2018-02-14 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Invitation to Morse Theory written by Liviu Nicolaescu and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mod Two Homology and Cohomology written by Jean-Claude Hausmann and published by Springer. This book was released on 2015-01-08 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology and homology modulo 2 helps the reader grasp more readily the basics of a major tool in algebraic topology. Compared to a more general approach to (co)homology this refreshing approach has many pedagogical advantages: 1. It leads more quickly to the essentials of the subject, 2. An absence of signs and orientation considerations simplifies the theory, 3. Computations and advanced applications can be presented at an earlier stage, 4. Simple geometrical interpretations of (co)chains. Mod 2 (co)homology was developed in the first quarter of the twentieth century as an alternative to integral homology, before both became particular cases of (co)homology with arbitrary coefficients. The first chapters of this book may serve as a basis for a graduate-level introductory course to (co)homology. Simplicial and singular mod 2 (co)homology are introduced, with their products and Steenrod squares, as well as equivariant cohomology. Classical applications include Brouwer's fixed point theorem, Poincaré duality, Borsuk-Ulam theorem, Hopf invariant, Smith theory, Kervaire invariant, etc. The cohomology of flag manifolds is treated in detail (without spectral sequences), including the relationship between Stiefel-Whitney classes and Schubert calculus. More recent developments are also covered, including topological complexity, face spaces, equivariant Morse theory, conjugation spaces, polygon spaces, amongst others. Each chapter ends with exercises, with some hints and answers at the end of the book.
Download or read book Advances in Applied and Computational Topology written by American Mathematical Society. Short Course on Computational Topology and published by American Mathematical Soc.. This book was released on 2012-07-05 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Progress in Industrial Mathematics at ECMI 2008 written by Alistair D. Fitt and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Mathematics of Data written by Michael W. Mahoney and published by American Mathematical Soc.. This book was released on 2018-11-15 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nothing provided
Download or read book Advanced Topics of Topology written by Francisco Bulnes and published by BoD – Books on Demand. This book was released on 2022-07-27 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology is an area of mathematics that establishes relations and transformations between spaces with a certain structure depending on their position and considering the structure of the ambient space where these relations exist. This book discusses various concepts and theories of topology, including diffeomorphisms, immersions, Hausdorff spaces, cobordisms, homotopy theory, symplectic manifolds, topology of quantum field theory, algebraic varieties, dimension theory, Koszul complexes, continuum theory, and metrizability, among others.
Download or read book Applications of Contact Geometry and Topology in Physics written by Arkady Leonidovich Kholodenko and published by World Scientific. This book was released on 2013 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although contact geometry and topology is briefly discussed in V I Arnol''d''s book Mathematical Methods of Classical Mechanics (Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges An Introduction to Contact Topology (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph Contact Geometry and Nonlinear Differential Equations (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous Landau-Lifshitz (L-L) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the L-L course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the L-L course some problems/exercises are formulated along the way and, again as in the L-L course, these are always supplemented by either solutions or by hints (with exact references). Unlike the L-L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text.
Download or read book Singularities Kagoshima 2017 Proceedings Of The 5th Franco japanese vietnamese Symposium On Singularities written by and published by World Scientific. This book was released on 2020-06-15 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a proceedings of the 5th Franco-Japanese-Vietnamese Symposium on Singularities held in Kagoshima during 27th October - 3rd November, 2017. The main theme of the symposium was Singularity Theory in a broad sense, including complex and real algebraic varieties, functions and mappings, and topology of singularities. The symposium was based on long-term interaction of singularity theorists in France, Japan, Vietnam and other countries. This volume includes three surveys of recent trends based on the lectures in the mini-school organized in the first two days of the symposium and articles presenting recent progress in Singularity Theory.
Download or read book Topological robotics motion planning in projective spaces written by Michael Farber and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topological Robotics Subspace Arrangements and Collision Free Motion Planning written by Michael Farber and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Motion Planning for Dynamic Agents written by Zain Anwar Ali and published by BoD – Books on Demand. This book was released on 2024-01-17 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, Motion Planning for Dynamic Agents, presents a thorough overview of current advancements and provides insights into the fascinating and vital field of aeronautics. It focuses on modern research and development, with an emphasis on dynamic agents. The chapters address a wide range of complex capabilities, including formation control, guidance and navigation, control techniques, wide-space coverage for inspection and exploration, and the best pathfinding in unknown territory. This book is a valuable resource for scholars, practitioners, and amateurs alike due to the variety of perspectives that are included, which help readers gain a sophisticated understanding of the difficulties and developments in the area of study.
