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Numerical algebraic geometry and algebraic kinematics

Published online by Cambridge University Press:  28 April 2011

Charles W. Wampler  and
Andrew J. Sommese
Charles W. Wampler
Affiliation:
General Motors Research and Development, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090-9055, USA E-mail: [email protected] URL: www.nd.edu/˜cwample1
Andrew J. Sommese
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618, USA E-mail: [email protected] URL: www.nd.edu/˜sommese
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Abstract

In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometry, which are primarily based on homotopy methods. We include a review of the main developments of recent years and outline some of the frontiers where further research is occurring. While numerical algebraic geometry applies broadly to any system of polynomial equations, algebraic kinematics provides a body of interesting examples for testing algorithms and for inspiring new avenues of work.

Type
Research Article
Information
Acta Numerica , Volume 20 , May 2011 , pp. 469 - 567
Copyright
Copyright © Cambridge University Press 2011

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