Grassmann-Cayley algebra and robotics
type: Item
instance of: scholarly article
title: Grassmann-Cayley algebra and robotics
zbMATH Open document ID: 0821.15020
DOI: 10.1007/BF01258296
author: Neil White
published in: Journal of Intelligent \& Robotic Systems
publication date: 1995-05-18T00:00:00Z
review text: Plücker coordinates are a suitable way to present lines in space for purposes of studying instantaneous motions of robot arms. In this paper the author presents an algebraic structure which is very useful for representing instantaneous motions of robots. He also presents applications to series-parallel mechanisms, rigidity of framework, and splines. He represents Grassmann-Cayley algebra in a concrete fashion, in terms of Plücker coordinates of subspaces. A synthetics geometric condition, expressed in the Grassmann-Caley algebra, and expanded by the shuffle formula, gives a bracket condition. This provides a translation of synthetic geometric conditions into invariant algebraic conditions. An important problem for several of his applications is the reverse translation, a problem is called Cayley factorization. He describes this problem and its role in computer-aided geometric reasoning.
Mathematics Subject Classification ID: 15A75
Mathematics Subject Classification ID: 70B15
zbMATH DE Number: 746196
zbMATH Keywords: bracket algebra
zbMATH Keywords: Plücker coordinates
zbMATH Keywords: motions of robot arms
zbMATH Keywords: series- parallel mechanisms
zbMATH Keywords: rigidity of framework
zbMATH Keywords: splines
zbMATH Keywords: Grassmann-Cayley algebra
zbMATH Keywords: bracket condition
zbMATH Keywords: Cayley factorization
zbMATH Keywords: computer-aided geometric reasoning
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
cites work: On the exterior calculus of invariant theory
cites work: Q3316741
cites work: On the Foundations of Combinatorial Theory: IX Combinatorial Methods in Invariant Theory
cites work: Q5539557
cites work: Q4185852
cites work: On the application of Buchberger's algorithm to automated geometry theorem proving
cites work: The Algebraic Geometry of Stresses in Frameworks
cites work: Multilinear Cayley factorization
cites work: Q3974994
description: scientific article; zbMATH DE number 746196