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Topological duality in humanoid robot dynamics

Published online by Cambridge University Press:  17 February 2009

V. Ivancevic  and
C. E. M. Pearce
V. Ivancevic
Affiliation:
Torson Productions Pty Ltd, Adelaide SA 5034, Australia.
C. E. M. Pearce
Affiliation:
Applied Mathematics Department, The University of Adelaide, Adelaide SA 5005, Australia.
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Abstract

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A humanoid robot system may be viewed as a collection of segments coupled at rotational joints which geometrically represent constrained rotational Lie groups. This allows a study of the dynamics of the motion of a humanoid robot. Several formulations are possible. In this paper, dual invariant topological structures are constructed and analyzed on the finite-dimensional manifolds associated with the humanoid motion. Both cohomology and homology structures are examined on the tangent (Lagrangian) as well as on the cotangent (Hamiltonian) bundles on the manifold of the humanoid motion configuration. represented by the toral Lie group. It is established all four topological structures give in essence the same description of humanoid dynamics. Practically this means that whichever of these approaches we use, ultimately we obtain the same mathematical results.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 2 , October 2001 , pp. 183 - 194
Copyright
Copyright © Australian Mathematical Society 2001

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