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Titlebook: Geometrical Methods in Robotics; J. M. Selig Textbook 19961st edition Springer Science+Business Media New York 1996 Grad.computing.differe

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书目名称Geometrical Methods in Robotics
编辑J. M. Selig
视频video
丛书名称Monographs in Computer Science
图书封面Titlebook: Geometrical Methods in Robotics;  J. M. Selig Textbook 19961st edition Springer Science+Business Media New York 1996 Grad.computing.differe
描述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 it
出版日期Textbook 19961st edition
关键词Grad; computing; differential geometry; engineering; kinematics; mathematics; robot; robotics
版次1
doihttps://doi.org/10.1007/978-1-4757-2484-4
isbn_ebook978-1-4757-2484-4Series ISSN 0172-603X Series E-ISSN 2512-5486
issn_series 0172-603X
copyrightSpringer Science+Business Media New York 1996
The information of publication is updating

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Line Geometry,een solved. Algebraic geometers think of ruled surfaces as line bundles over a curve or even more abstract descriptions. Differential geometers usually worry about the extrinsic geometry of ruled surfaces—that is, how such surfaces can sit in three dimensions—their curvature, and so forth. Symplecti
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Representation Theory,eady. However, we want to be more systematic here and apply some of the large modern subject of representation theory to robotics. An excellent introduction to representation theory can be found in Fulton and Harris [24]. We begin by making some formal definitions.
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Clifford Algebra, algebras of anti-symmetric tensors. Originally, both were developed for facilitating geometrical computations, and indeed Grassmann algebras have been recently rediscovered by computer scientists for performing calculations in computational geometry. In fact, as we will see a little later, the only
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The Study Quadric,specify the position of the body by attaching a coordinate frame to it. He called these ‘points’ ., which is Greek for .. Clifford’s biquaternions were then used as coordinates for the space. As we saw in section 9.3, using the biquaternion representation, the elements of the group of rigid body mot
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