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Quaternion representations of the O+(3) group, and their applications in robotics

✍ Scribed by J.F. Bitó; G.Y. Eröss; J.K. Tar

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
602 KB
Volume
4
Category
Article
ISSN
0952-1976

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✦ Synopsis

algebraic methods for solving different mathematical tasks have found widespread applications in theoretical physics and in several technical applications. Though group theory can be used to achieve the most simple and transparent formulation of different tasks, it is not very well known by engineers. The aim of this paper is to discuss quaternion representations of the 0 +(3) Lie group from the aspect of robotics. The main features of these representations, as well as their advantages over the pure 3 x 3 matrix (self-)representation, are discussed in the formulation and solution of the direct and inverse kinematic tasks for robots of general wrist-joint structure. To illustrate the convenience of quaternion formulations a particular solution of the inverse kinematic task has been developed on the basis of the concept of non-Euclidean (curved) spaces. A possible Hopfield-type neural-network application appropriate to the proposed solution is also considered.

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