Computer Aided Geometric Design ( IF 1.5 ) Pub Date : 2020-05-05 , DOI: 10.1016/j.cagd.2020.101872 Yuanqing Wu , Marco Carricato
Mechanisms and robots often share the following fundamental property: the instantaneous twist space generated by the end-effector at a generic pose is a rigidly-displaced copy of the one generated at the home configuration, i.e., the tangent spaces at all points of its motion manifold (a manifold of the Lie group of rigid displacements ) are mutually congruent. A manifold of this kind, hereafter denoted as persistent, can be seen as the envelope of a persistent twist subspace rigidly moving in . In this paper, we shall summarize three important classes of persistent manifolds that have so far been discovered and systematically investigated in the literature, namely the Lie subgroups, the persistent product-of-exponential (POE) manifolds, and the symmetric subspaces. In each case, the persistence property arises from a distinct manifold structure, which dictates the ensuing classification and underlies the framework for the synthesis of mechanical devices that are capable of generating such manifolds. In this regard, we attempt to offer a guideline to classification and mechanism synthesis of persistent manifolds for a general audience.
中文翻译:
特殊欧氏群SE(3)的持久流形:综述
机械和机器人通常具有以下基本属性:末端执行器在通用姿势下产生的瞬时扭转空间是在原始配置下产生的刚性位移的副本,即在其运动的所有点处的切线空间歧管(Lie群的刚性位移的歧管 )是相互一致的。这种歧管,以下称为持久性歧管,可以看作是刚性扭曲的持久子空间的包络。在本文中,我们将总结迄今为止在文献中发现并进行系统研究的三类重要的持久流形,即李子群,持久指数乘积(POE)流形和对称子空间。在每种情况下,持久性属性都来自于独特的歧管结构,该结构决定了随后的分类,并且奠定了能够生成此类歧管的机械设备合成的框架的基础。在这方面,我们尝试为普通观众提供有关持久流形的分类和机制综合的指南。