Progress in Industrial Mathematics at ECMI 2008
Progress in Industrial Mathematics at ECMI 2008
复制标题
ECMI 2008 工业数学进展
DOI：
10.1007/978-3-642-12110-4_134
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Farber M
中科院分区：
文献类型：
--
作者：
Farber M
利用代数拓扑学的方法分析了机器人运动规划算法的结构。力学系统的导航复杂性是通过依赖于位形空间X的同伦类型的数值不变量TC（X）来度量的。TC（X）的计算使用各种拓扑工具，包括上同调代数和上同调运算。本文是一个简短的调查介绍这些主题的应用和工业数学家的社会。该方法说明了多个移动对象的同时控制问题的应用程序。
Methods of algebraic topology are used to analyze the structure of motion planning algorithms in robotics. Navigational complexity of a mechanical system is measured by a numerical invariant TC(X) depending on the homotopy type of the configuration spaceX. Computations of TC(X) use various topological tools including cohomology algebras and cohomology operations. This paper is a brief survey introducing these topics to the community of applied and industrial mathematicians. The method is illustrated by applications to problems of simultaneous control of multiple moving objects.