Computing saddle graphs via homotopy continuation for the approximate synthesis of mechanisms
Computing saddle graphs via homotopy continuation for the approximate synthesis of mechanisms
复制标题
通过同伦延拓计算鞍图以近似综合机制
DOI：
10.1016/j.mechmachtheory.2022.104932
复制
发表时间：
2022
影响因子：
5.2
通讯作者：
Hauenstein, Jonathan D.
中科院分区：
文献类型：
--
作者：
Baskar, Aravind;Plecnik, Mark;Hauenstein, Jonathan D.
本文提出了一种机构近似运动综合的方法，该方法计算一个图，该图将目标函数的极小值标识为顶点，并将它们之间的连接标识为边。这样的图被交互地呈现给设计者，由此边被连续地遍历以在最小值之间导航设计候选族。在探索设计权衡的过程中，会根据辅助考虑不断地对候选人进行评估。相关的设计规范往往因应用而异，要么不清楚如何纳入目标，要么明确但对功能评估的复杂性有很大影响。计算上述图首先通过多项式同伦延拓寻找目标函数的所有极小点和鞍点。最小化其最大目标值的极小值之间的联系必须通过鞍点才能做到这一点。因此，在收集鞍座后，每个鞍座在其最小特征方向上被双向扰动，以播种连接两个极小值的梯度下降路径。已发现的极小值之间的联系被组织成一个图，其中的边对应于梯度下降路径。
An approach for approximate kinematic synthesis of mechanisms is proposed in this paper which computes a graph that identifies minima of an objective function as vertices and connections between them as edges. Such a graph is interactively presented to a designer, whereby edges are continuously traversed to navigate families of design candidates in between minima. Candidates are evaluated continuously according to auxiliary considerations for the exploration of design trade-offs. Relevant design specifications tend to be particular per application and are either unclear as how to incorporate into an objective, or clear but with great consequence to the complexity of function evaluation. Computing the aforementioned graphs begins with finding all minima and saddles of an objective function through polynomial homotopy continuation. Connections between minima that minimize their maximum objective value must pass through a saddle to do so. Therefore, after gathering saddles, each is perturbed both ways in its least eigendirection to seed gradient descent paths which connect two minima when pieced together. Discovered connections between minima are organized into a graph, where edges correspond to gradient descent paths.
登录
查看更多内容
一种计算运动学综合中出现的大型多项式方程组有限根的算法
影响因子：
5.2
作者：
A. Baskar;S. Bandyopadhyay
通讯作者：
S. Bandyopadhyay
使用随机单峰循环的斯蒂芬森型六条定时曲线发生器的综合
DOI：
--
发表时间：
2021
期刊：
影响因子：
--
作者：
A. Baskar;Mark M. Plecnik
通讯作者：
Mark M. Plecnik
影响因子：
5.2
作者：
S. Krishnamurty;D. Turcic
通讯作者：
D. Turcic
DOI：
10.1007/978-3-030-91352-6_4
发表时间：
2020
期刊：
Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation
影响因子：
--
作者：
J. Hauenstein;Samantha N. Sherman
通讯作者：
Samantha N. Sherman
Stephenson-III 运动发生器的无缺陷合成
DOI：
10.1243/09544062jmes994
发表时间：
2008
期刊：
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
影响因子：
--
作者：
W. Hwang;Y
通讯作者：
Y