Algebraic Geometry For Robotics And Control Theory
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Algebraic Geometry For Robotics And Control Theory
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Author : Laura Menini
language : en
Publisher: World Scientific
Release Date : 2021-09-02
Algebraic Geometry For Robotics And Control Theory written by Laura Menini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-02 with Technology & Engineering categories.
The development of inexpensive and fast computers, coupled with the discovery of efficient algorithms for dealing with polynomial equations, has enabled exciting new applications of algebraic geometry and commutative algebra. Algebraic Geometry for Robotics and Control Theory shows how tools borrowed from these two fields can be efficiently employed to solve relevant problem arising in robotics and control theory.After a brief introduction to various algebraic objects and techniques, the book first covers a wide variety of topics concerning control theory, robotics, and their applications. Specifically this book shows how these computational and theoretical methods can be coupled with classical control techniques to: solve the inverse kinematics of robotic arms; design observers for nonlinear systems; solve systems of polynomial equalities and inequalities; plan the motion of mobile robots; analyze Boolean networks; solve (possibly, multi-objective) optimization problems; characterize the robustness of linear; time-invariant plants; and certify positivity of polynomials.
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.
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.
* Provides an elegant introduction to the geometric concepts that are important to applications in robotics * Includes significant state-of-the art material that reflects important advances, connecting robotics back to mathematical fundamentals in group theory and geometry * An invaluable reference that serves a wide audience of grad students and researchers in mechanical engineering, computer science, and applied mathematics
Methods Of Algebraic Geometry In Control Theory
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Author : Peter L. Falb
language : en
Publisher:
Release Date : 1990
Methods Of Algebraic Geometry In Control Theory written by Peter L. Falb and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Control theory categories.
Geometric Control Theory And Sub Riemannian Geometry
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Author : Gianna Stefani
language : en
Publisher: Springer
Release Date : 2014-06-05
Geometric Control Theory And Sub Riemannian Geometry written by Gianna Stefani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-05 with Mathematics categories.
Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.
Geometric Control Of Mechanical Systems
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Author : Francesco Bullo
language : en
Publisher: Springer
Release Date : 2019-06-12
Geometric Control Of Mechanical Systems written by Francesco Bullo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-12 with Science categories.
The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.
Geometric And Numerical Foundations Of Movements
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Author : Jean-Paul Laumond
language : en
Publisher: Springer
Release Date : 2017-05-02
Geometric And Numerical Foundations Of Movements written by Jean-Paul Laumond and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-02 with Technology & Engineering categories.
This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “ Geometric and Numerical Foundations of Movements ” held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.
2nd Ima Conference On Mathematics Of Robotics
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Author : William Holderbaum
language : en
Publisher: Springer Nature
Release Date : 2021-11-20
2nd Ima Conference On Mathematics Of Robotics written by William Holderbaum and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-20 with Technology & Engineering categories.
This book highlights the mathematical depth and sophistication of techniques used in different areas of robotics. Each chapter is a peer-reviewed version of a paper presented during the 2021 IMA Conference on the Mathematics of Robotics, held online September 8–10, 2021. The conference gave a platform to researchers with fundamental contributions and for academic and to share new ideas. The book illustrates some of the current interest in advanced mathematics and robotics such as algebraic geometry, tropical geometry, monodromy and homotopy continuation methods applied to areas such as kinematics, path planning, swam robotics, dynamics and control. It is hoped that the conference and this publications will stimulate further related mathematical research in robotics.
Control Theory Of Robotic Systems
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Author : J M Skowronski
language : en
Publisher: World Scientific
Release Date : 1989-08-01
Control Theory Of Robotic Systems written by J M Skowronski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-01 with Computers categories.
Automated manufacturing is the topic of the day in industry and thus also in R&D investigation in both industrial laboratories and academia. The core of such studies lies in systems of robotic manipulators, with control of such systems for stability, effective goal reaching and coordination (timing, avoidance of collision) being an essential part of it. The manipulators must work at high speed and under considerable payloads which require nonlinear modelling. Their work is subject to bounded uncertainty in many parameters but precision must be secured. This book gives the theoretic base and specific algorithms for control, attaining the objectives under the above features. The algorithms given are in closed form, which makes for fast on-board computing.The book deals with its subject of systems of robots and their coordination control on a fundamental basis, using realistic untruncated models. It will be of lasting interest compared to texts dealing with details of the design of the day.