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Some Geometry for Robot Kinematics

by

J.M. Selig, London South Bank University.
DAte: 26th January, 2023, Time: 14:00.
Place: Dokuz Eylül Üniv., Tınaztepe Yerleşkesi, Fen Fak. Matematik Böl.

Abstract:The talk will begin with a brief review of dual quaternions and the realisation of the group of rigid-body displacements by the Study quadric. Next we look at some linear subspaces of the Study quadric and their interpretation as sets of displacements. Following this we will describe some sets of displacements that are intersections of the Study quadric with linear subspaces of the surrounding P^7. Then we will discuss some Segre varieties. These can be realised by simple serial linkages. A final extended example shows how some of these ideas can be used to solve problems in the theory of mechanisms.

Quaternions, Dual Quaternions and Clifford algebras

by

J.M. Selig, London South Bank University.
Date: 24th January, 2023, Time: 14:00.
Place: Dokuz Eylül Üniv., Tınaztepe Yerleşkesi, Fen Fak. Matematik Böl.

Abstract:After a brief review of Hamilton’s quaternions and how they can be used to represent rotations, Clifford’s dual quaternions will be discussed. The use of this algebra to represent rigid-body displacements will be explained. As will the relation to the Study quadric. The representation of twists, infinitesimal rigid-body displacements, will also be considered. Finally, the notion of Clifford algebras will be introduced and various examples will be considered. In particular, examples rep-resenting the algebra of 3-dimensional Euclidean geometry will be outlined.