Robotic problems over a configurational manifold of vector parameters and dual vector parameters
type: Item
instance of: scholarly article
title: Robotic problems over a configurational manifold of vector parameters and dual vector parameters
zbMATH Open document ID: 0820.93045
DOI: 10.1007/BF01258298
published in: Journal of Intelligent \& Robotic Systems
publication date: 1995-04-20T00:00:00Z
review text: The kinematics of a manipulator involves the Euclidean group. A vector parametrization of SO(3), obtained using the Cayley transformation, allows to introduce a group action of the Lie group of vector parameters (the composition law is: \(c.d = {c + d + c \wedge d\over 1 - c^ t d}\) where \(c\), \(d\) belong to \(\mathbb{R}^ 3\)) on the trivialized tangent bundle of SO(3) (which is also a Lie group). An other description using Plücker coordinates allow to use revolute and prismatic joint variables of the manipulator and to introduce a ``dual'' matrix and vector notation. The same vector parametrization is used and leads also to an elegant and efficient description of manipulator kinematics.
Mathematics Subject Classification ID: 93C85
Mathematics Subject Classification ID: 22E99
Mathematics Subject Classification ID: 93B40
zbMATH DE Number: 746198
zbMATH Keywords: dual matrix
zbMATH Keywords: manipulator
zbMATH Keywords: parametrization of SO(3)
zbMATH Keywords: revolute and prismatic joint variables
zbMATH Keywords: kinematics
author: Clementina Mladenova
reviewed by: A. Akutowicz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 746198