Numerical algebraic geometry and algebraic kinematics
Numerical algebraic geometry and algebraic kinematics
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DOI：
10.1017/s0962492911000067
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发表时间：
2011-01-01
期刊：
影响因子：
--
通讯作者：
Sommese, Andrew J.
中科院分区：
文献类型：
--
作者：
Wampler, Charles W.;Sommese, Andrew J.
在本文中，介绍了代数运动学的基本结构（连杆、关节和机构空间）。这为运动学研究中感兴趣的多种问题提供了一个通用模式。一旦问题被放入这个代数框架中，它们就可以用代数几何的工具来解决。我们特别回顾了主要基于同伦方法的数值代数几何技术。我们回顾了近年来的主要发展，并概述了正在进行进一步研究的一些前沿领域。虽然数值代数几何广泛适用于任何多项式方程组，但代数运动学为测试算法和激发新的工作途径提供了大量有趣的例子。
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.