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Invitation to topological robotics /

Farber, Michael, (1951-)

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Invitation to topological robotics /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Invitation to topological robotics // Michael Farber.
作者:	Farber, Michael,
出版者:	Zürich :European Mathematical Society, : c2008.,
面頁冊數:	x, 132 p. :ill. ;24 cm.
標題:	Topology. -
ISBN:	9783037190548 (pbk.) :

Invitation to topological robotics /
Farber, Michael,1951-

Invitation to topological robotics /Michael Farber. - Zürich :European Mathematical Society,c2008. - x, 132 p. :ill. ;24 cm. - Zurich lectures in advanced mathematics. - Zurich lectures in advanced mathematics..

Includes bibliographical references (p. [127]-132) and index.

"The book discusses several selected topics of a new emerging area of research lying on the interface between topology and engineering. The first main topic of the book 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 we apply a new technique of Morse theory in the presence of an involution. A significant result of topology of linkages presented in the 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. The 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 of the book is topology of configuration spaces associated to polyhedra. The book 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 we study the knot theory of a robot arm focusing on a recent important result of R. Connelly, E. Demain and G. Rote. Finally, the book 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."--BOOK JACKET.

ISBN: 9783037190548 (pbk.) :US39.00

LCCN: 2009419150Subjects--Topical Terms:

522026
Topology.

LC Class. No.: QA611.3 / .F37 2008

Invitation to topological robotics /
LDR:02249cam a2200205 a 4500 001 1266111
003 OCoLC
005 20120724033106.0
008 120822s2008 sz a b 001 0 eng c
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020 $a 9783037190548 (pbk.) : $c US39.00
020 $a 303719054X (pbk.)
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050 # 4 $a QA611.3 $b .F37 2008
100 1 $a Farber, Michael, $d 1951- $3 725845
245 1 0 $a Invitation to topological robotics / $c Michael Farber.
260 # $a Zürich : $b European Mathematical Society, $c c2008.
300 $a x, 132 p. : $b ill. ; $c 24 cm.
490 1 0 $a Zurich lectures in advanced mathematics
504 $a Includes bibliographical references (p. [127]-132) and index.
520 1 $a "The book discusses several selected topics of a new emerging area of research lying on the interface between topology and engineering. The first main topic of the book 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 we apply a new technique of Morse theory in the presence of an involution. A significant result of topology of linkages presented in the 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. The 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 of the book is topology of configuration spaces associated to polyhedra. The book 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 we study the knot theory of a robot arm focusing on a recent important result of R. Connelly, E. Demain and G. Rote. Finally, the book 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."--BOOK JACKET.
650 # 0 $a Topology. $3 522026
650 # 0 $a Robotics $x Mathematics. $3 1533594
650 # 0 $a Configuration space. $3 713541
830 0 $a Zurich lectures in advanced mathematics. $3 935060