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 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 Geometry Topology and Mathematical Physics written by V. M. Buchstaber and published by American Mathematical Soc.. This book was released on 2004 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 VI written by Michael Erdmann and published by Springer Science & Business Media. This book was released on 2005-06-23 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robot algorithms are abstractions of computational processes that control or reason about motion and perception in the physical world. Because actions in the physical world are subject to physical laws and geometric constraints, the design and analysis of robot algorithms raise a unique combination of questions in control theory, computational and differential geometry, and computer science. Algorithms serve as a unifying theme in the multi-disciplinary field of robotics. This volume consists of selected contributions to the sixth Workshop on the Algorithmic Foundations of Robotics. This is a highly competitive meeting of experts in the field of algorithmic issues related to robotics and automation.
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 Planning Algorithms written by Steven M. LaValle and published by Cambridge University Press. This book was released on 2006-05-29 with total page 1029 pages. Available in PDF, EPUB and Kindle. Book excerpt: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning, but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the 'configuration spaces' of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. This text and reference is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.
Download or read book Braids written by A. Jon Berrick and published by World Scientific. This book was released on 2010 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tutorial on the braid groups / Dale Rolfsen -- Simplicial objects and homotopy groups / Jie Wu -- Introduction to configuration spaces and their applications / Frederick R. Cohen -- Configuration spaces, braids, and robotics / Robert Ghrist -- Braids and magnetic fields / Mitchell A. Berger -- Braid group cryptography / David Garber
Download or read book Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology written by Paul Biran and published by Springer Science & Business Media. This book was released on 2006-02-12 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers collected in this volume are contributions to the 43rd session of the Seminaire ́ de mathematiques ́ superieures ́ (SMS) on “Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology.” This session took place at the Universite ́ de Montreal ́ in July 2004 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together young researchers from various parts of the world and to present to them some of the most signi cant recent advances in these areas. More than 77 mathematicians from 17 countries followed the 12 series of lectures and participated in the lively exchange of ideas. The lectures covered an ample spectrum of subjects which are re ected in the present volume: Morse theory and related techniques in in nite dim- sional spaces, Floer theory and its recent extensions and generalizations, Morse and Floer theory in relation to string topology, generating functions, structure of the group of Hamiltonian di?eomorphisms and related dynamical problems, applications to robotics and many others. We thank all our main speakers for their stimulating lectures and all p- ticipants for creating a friendly atmosphere during the meeting. We also thank Ms. Diane Belanger ́ , our administrative assistant, for her help with the organi- tion and Mr. Andre ́ Montpetit, our technical editor, for his help in the preparation of the volume.
Download or read book Configuration Spaces written by Filippo Callegaro and published by Springer. This book was released on 2016-08-27 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014. With combinatorial techniques as the central theme, it focuses on recent developments in configuration spaces from various perspectives. It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology.
Download or read book Optimized Motion Planning written by Cherif Ahrikencheikh and published by Wiley-Interscience. This book was released on 1994-10-14 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first handbook to the practical specifics of motion planning, Optimized-Motion Planning offers design engineers methods and insights for solving real motion planning problems in a 3-dimensional space. Complete with a disk of software programs, this unique guide allows users to design, test, and implement possible solutions, useful in a host of contexts, especially tool path planning. Beginning with a brief overview of the general class of problems examined within the book as well as available solution techniques, Part 1 familiarizes the reader with the conceptual threads that underlie each approach. This early discussion also considers the specific applications of each technique as well as its computational efficiency. Part 2 illustrates basic problem-solving methodology by considering the case of a point moving between stationary polygons in a plane. This section features algorithms for data organization and storage, the concepts of passage networks and feasibility charts, as well as the path optimization algorithm. Elaborating on the problematic model described in Part 2, Part 3 develops an algorithm for optimizing the motion of a point between stationary polyhedra in a 3-dimensional space. This algorithm is first applied to the case of nonpoint objects moving between obstacles that can be stationary or moving with known patterns. It's then used in connection with the extensively investigated problem of motion planning for multilink manipulators.
Download or read book Advances in Algebraic Geometry Motivated by Physics written by Emma Previato and published by American Mathematical Soc.. This book was released on 2001 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our knowledge of objects of algebraic geometry such as moduli of curves, (real) Schubert classes, fundamental groups of complements of hyperplane arrangements, toric varieties, and variation of Hodge structures, has been enhanced recently by ideas and constructions of quantum field theory, such as mirror symmetry, Gromov-Witten invariants, quantum cohomology, and gravitational descendants. These are some of the themes of this refereed collection of papers, which grew out of the special session, ``Enumerative Geometry in Physics,'' held at the AMS meeting in Lowell, MA, April 2000. This session brought together mathematicians and physicists who reported on the latest results and open questions; all the abstracts are included as an Appendix, and also included are papers by some who could not attend. The collection provides an overview of state-of-the-art tools, links that connect classical and modern problems, and the latest knowledge available.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Fast Collision free Motion Planning of a Mobile Robot written by Xian Chang and published by . This book was released on 1993 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Practical Motion Planning in Robotics written by Kamal Gupta and published by Chichester, England ; Toronto : J. Wiley. This book was released on 1998-10-15 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practical Motion Planning in Robotics Current Approaches and Future Directions Edited by Kamal Gupta Simon Fraser University, Burnaby, Canada Angel P. del Pobil Jaume-l University, Castellon, Spain Designed to bridge the gap between research and industry, Practical Motion Planning in Robotics brings theoretical advances to bear on real-world applications. Capitalizing on recent progress, this comprehensive study emphasizes the practical aspects of techniques for collision detection, obstacle avoidance, path planning and manipulation planning. The broad approach spans both model- and sensor-based motion planning, collision detection and geometric complexity, and future directions. Features include: - Review of state-of-the-art techniques and coverage of the main issues to be considered in the development of motion planners for use in real applications - Focus on gross motion planning for articulated arms enabling robots to perform non-contact tasks with relatively high tolerances plus brief consideration of mobile robots - The use of efficient algorithms to tackle incremental changes in the environment - Illlustration of robot motion planning applications in virtual prototyping and the shipbuilding industry - Demonstration of efficient path planners combining both local and global planning approaches in conjunction with efficient techniques for collision detection and distance computations - International contributions from academia and industry Combining theory and practice, this timely book will appeal to academic researchers and practising engineers in the fields of robotic systems, mechatronics and computer science.
