Geometrical Methods In Robotics

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Geometrical Methods In Robotics

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Author : J.M. Selig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Geometrical Methods In Robotics written by J.M. Selig 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 2013-03-09 with Computers categories.

The main aim of this book is to introduce Lie groups and allied algebraic and geometric concepts to a robotics audience. These topics seem to be quite fashionable at the moment, but most of the robotics books that touch on these topics tend to treat Lie groups as little more than a fancy notation. I hope to show the power and elegance of these methods as they apply to problems in robotics. A subsidiary aim of the book is to reintroduce some old ideas by describing them in modem notation, particularly Study's Quadric-a description of the group of rigid motions in three dimensions as an algebraic variety (well, actually an open subset in an algebraic variety)-as well as some of the less well known aspects of Ball's theory of screws. In the first four chapters, a careful exposition of the theory of Lie groups and their Lie algebras is given. Except for the simplest examples, all examples used to illustrate these ideas are taken from robotics. So, unlike most standard texts on Lie groups, emphasis is placed on a group that is not semi-simple-the group of proper Euclidean motions in three dimensions. In particular, the continuous subgroups of this group are found, and the elements of its Lie algebra are identified with the surfaces of the lower Reuleaux pairs. These surfaces were first identified by Reuleaux in the latter half of the 19th century.

Geometric Fundamentals Of Robotics

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Author : J.M. Selig
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-13

Geometric Fundamentals Of Robotics written by J.M. Selig 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 2007-12-13 with Technology & Engineering categories.

Geometric Fundamentals of Robotics provides an elegant introduction to the geometric concepts that are important to applications in robotics. This second edition is still unique in providing a deep understanding of the subject: rather than focusing on computational results in kinematics and robotics, it includes significant state-of-the-art material that reflects important advances in the field, connecting robotics back to mathematical fundamentals in group theory and geometry. Geometric Fundamentals of Robotics serves a wide audience of graduate students as well as researchers in a variety of areas, notably mechanical engineering, computer science, and applied mathematics. It is also an invaluable reference text.

Geometric Methods And Applications

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Author : Jean Gallier
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-04

Geometric Methods And Applications written by Jean Gallier 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 2011-06-04 with Mathematics categories.

This book is an introduction to the fundamental concepts and tools needed for solving problems of a geometric nature using a computer. It attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, robotics, or machine learning. This book covers the following topics: affine geometry, projective geometry, Euclidean geometry, convex sets, SVD and principal component analysis, manifolds and Lie groups, quadratic optimization, basics of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). Some practical applications of the concepts presented in this book include computer vision, more specifically contour grouping, motion interpolation, and robot kinematics. In this extensively updated second edition, more material on convex sets, Farkas’s lemma, quadratic optimization and the Schur complement have been added. The chapter on SVD has been greatly expanded and now includes a presentation of PCA. The book is well illustrated and has chapter summaries and a large number of exercises throughout. It will be of interest to a wide audience including computer scientists, mathematicians, and engineers. Reviews of first edition: "Gallier's book will be a useful source for anyone interested in applications of geometrical methods to solve problems that arise in various branches of engineering. It may help to develop the sophisticated concepts from the more advanced parts of geometry into useful tools for applications." (Mathematical Reviews, 2001) "...it will be useful as a reference book for postgraduates wishing to find the connection between their current problem and the underlying geometry." (The Australian Mathematical Society, 2001)

Geometrical Foundations Of Robotics

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Author : J. M. Selig
language : en
Publisher: World Scientific
Release Date : 2000

Geometrical Foundations Of Robotics written by J. M. Selig and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Computers categories.

This book is a collection of talks presented at the 1998 IEEE International Conference on Robotics and Automation. Broadly, the meeting discussed the application of modern geometrical methods to problems in robotics. There are now a few textbooks in this area and more papers in the literature. The aim of this book is to introduce these ideas, their simplicity and power, to a wider audience. The first three chapters give an introduction to the Lie group and Lie algebras. The focus is on the group of rigid body transformations in space, namely the Lie group which is fundamental to robotics. The following chapters provide an overview of some of the most up-to-date work in the field of geometrical methods in robotics and have been written by some of the leading researchers in the field. The applications addressed cover the design of robot kinematics, the analysis of singularities in robots and mechanisms, and a geometric view of some computational issues.

Geometric Algebra Applications Vol Ii

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Author : Eduardo Bayro-Corrochano
language : en
Publisher: Springer Nature
Release Date : 2020-06-19

Geometric Algebra Applications Vol Ii written by Eduardo Bayro-Corrochano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-19 with Mathematics categories.

This book presents a unified mathematical treatment of diverse problems in the general domain of robotics and associated fields using Clifford or geometric alge- bra. By addressing a wide spectrum of problems in a common language, it offers both fresh insights and new solutions that are useful to scientists and engineers working in areas related with robotics. It introduces non-specialists to Clifford and geometric algebra, and provides ex- amples to help readers learn how to compute using geometric entities and geomet- ric formulations. It also includes an in-depth study of applications of Lie group theory, Lie algebra, spinors and versors and the algebra of incidence using the universal geometric algebra generated by reciprocal null cones. Featuring a detailed study of kinematics, differential kinematics and dynamics using geometric algebra, the book also develops Euler Lagrange and Hamiltoni- ans equations for dynamics using conformal geometric algebra, and the recursive Newton-Euler using screw theory in the motor algebra framework. Further, it comprehensively explores robot modeling and nonlinear controllers, and discusses several applications in computer vision, graphics, neurocomputing, quantum com- puting, robotics and control engineering using the geometric algebra framework. The book also includes over 200 exercises and tips for the development of future computer software packages for extensive calculations in geometric algebra, and a entire section focusing on how to write the subroutines in C++, Matlab and Maple to carry out efficient geometric computations in the geometric algebra framework. Lastly, it shows how program code can be optimized for real-time computations. An essential resource for applied physicists, computer scientists, AI researchers, roboticists and mechanical and electrical engineers, the book clarifies and demon- strates the importance of geometric computing for building autonomous systems to advance cognitive systems research.

Polyhedral And Algebraic Methods In Computational Geometry

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Author : Michael Joswig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-04

Polyhedral And Algebraic Methods In Computational Geometry written by Michael Joswig 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 2013-01-04 with Mathematics categories.

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Springer Handbook Of Robotics

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Author : Bruno Siciliano
language : en
Publisher: Springer
Release Date : 2016-07-27

Springer Handbook Of Robotics written by Bruno Siciliano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-27 with Technology & Engineering categories.

The second edition of this handbook provides a state-of-the-art overview on the various aspects in the rapidly developing field of robotics. Reaching for the human frontier, robotics is vigorously engaged in the growing challenges of new emerging domains. Interacting, exploring, and working with humans, the new generation of robots will increasingly touch people and their lives. The credible prospect of practical robots among humans is the result of the scientific endeavour of a half a century of robotic developments that established robotics as a modern scientific discipline. The ongoing vibrant expansion and strong growth of the field during the last decade has fueled this second edition of the Springer Handbook of Robotics. The first edition of the handbook soon became a landmark in robotics publishing and won the American Association of Publishers PROSE Award for Excellence in Physical Sciences & Mathematics as well as the organization’s Award for Engineering & Technology. The second edition of the handbook, edited by two internationally renowned scientists with the support of an outstanding team of seven part editors and more than 200 authors, continues to be an authoritative reference for robotics researchers, newcomers to the field, and scholars from related disciplines. The contents have been restructured to achieve four main objectives: the enlargement of foundational topics for robotics, the enlightenment of design of various types of robotic systems, the extension of the treatment on robots moving in the environment, and the enrichment of advanced robotics applications. Further to an extensive update, fifteen new chapters have been introduced on emerging topics, and a new generation of authors have joined the handbook’s team. A novel addition to the second edition is a comprehensive collection of multimedia references to more than 700 videos, which bring valuable insight into the contents. The videos can be viewed directly augmented into the text with a smartphone or tablet using a unique and specially designed app. Springer Handbook of Robotics Multimedia Extension Portal: http://handbookofrobotics.org/

Handbook Of Geometric Computing

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Author : Eduardo Bayro Corrochano
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-06

Handbook Of Geometric Computing written by Eduardo Bayro Corrochano 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 2005-12-06 with Computers categories.

Many computer scientists, engineers, applied mathematicians, and physicists use geometry theory and geometric computing methods in the design of perception-action systems, intelligent autonomous systems, and man-machine interfaces. This handbook brings together the most recent advances in the application of geometric computing for building such systems, with contributions from leading experts in the important fields of neuroscience, neural networks, image processing, pattern recognition, computer vision, uncertainty in geometric computations, conformal computational geometry, computer graphics and visualization, medical imagery, geometry and robotics, and reaching and motion planning. For the first time, the various methods are presented in a comprehensive, unified manner. This handbook is highly recommended for postgraduate students and researchers working on applications such as automated learning; geometric and fuzzy reasoning; human-like artificial vision; tele-operation; space maneuvering; haptics; rescue robots; man-machine interfaces; tele-immersion; computer- and robotics-aided neurosurgery or orthopedics; the assembly and design of humanoids; and systems for metalevel reasoning.

A Mathematical Introduction To Robotic Manipulation

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Author : Richard M. Murray
language : en
Publisher: CRC Press
Release Date : 2017-12-14

A Mathematical Introduction To Robotic Manipulation written by Richard M. Murray and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-14 with Technology & Engineering categories.

A Mathematical Introduction to Robotic Manipulation presents a mathematical formulation of the kinematics, dynamics, and control of robot manipulators. It uses an elegant set of mathematical tools that emphasizes the geometry of robot motion and allows a large class of robotic manipulation problems to be analyzed within a unified framework. The foundation of the book is a derivation of robot kinematics using the product of the exponentials formula. The authors explore the kinematics of open-chain manipulators and multifingered robot hands, present an analysis of the dynamics and control of robot systems, discuss the specification and control of internal forces and internal motions, and address the implications of the nonholonomic nature of rolling contact are addressed, as well. The wealth of information, numerous examples, and exercises make A Mathematical Introduction to Robotic Manipulation valuable as both a reference for robotics researchers and a text for students in advanced robotics courses.