论文标题
利用单构莫尼罗术在统计上估计解决方案的数量
Using monodromy to statistically estimate the number of solutions
论文作者
论文摘要
运动学中链接的综合问题通常会产生大型结构化的参数化多项式系统，这些系统的解决方案通常比传统上限所暗示的要少得多。本文介绍了用于估计这种参数化多项式系统的通用解决方案数量的统计模型。新方法将参数同型的成功比率扩展到了使用单片循环以及添加痕量测试，该痕量测试提供了验证所有解决方案的停止标准。举了几个示例，证明了该方法，包括瓦特I六杆运动产生问题。
Synthesis problems for linkages in kinematics often yield large structured parameterized polynomial systems which generically have far fewer solutions than traditional upper bounds would suggest. This paper describes statistical models for estimating the generic number of solutions of such parameterized polynomial systems. The new approach extends previous work on success ratios of parameter homotopies to using monodromy loops as well as the addition of a trace test that provides a stopping criterion for validating that all solutions have been found. Several examples are presented demonstrating the method including Watt I six-bar motion generation problems.
