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On avoiding singularities in redundant robot kinematics

Published online by Cambridge University Press:  09 March 2009

Krzysztof Tchoń  and
Aleksander Matuszok
Krzysztof Tchoń
Affiliation:
Institute of Engineering Cybernetics, Technical University of Wroclaw, ul.Janiszewskiego 11/17, 50-372 Wroclaw (Poland)
Aleksander Matuszok
Affiliation:
Institute of Engineering Cybernetics, Technical University of Wroclaw, ul.Janiszewskiego 11/17, 50-372 Wroclaw (Poland)
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Summary

For redundant robot kinematics with a degree of redundancy 1 a self-motion vector field is examined whose equilibrium points lie at singular configurations of the kinematics, and whose orbits determine the self-motion manifolds. It is proved that the self-motion vector field is divergence-free. Locally, around singular configurations of corank 1, the self-motion vector field defines a 2-dimensional Hamiltonian dynamical system. An analysis of the phase portrait of this system in a neighbourhood of a singular configuration solves completely the question of avoidability or unavoidability of this configuration. Complementarily, sufficient conditions for avoidability and unavoidability are proposed in an analytic form involving the self-motion Hamilton function. The approach is illustrated with examples. A connection with normal forms of kinematics is established.

Keywords

Redundant kinematicsSingular configurationSingularity avoidanceSelf-motion manifoldVector fieldHamiltonian dynamical system
Type
Articles
Information
Robotica , Volume 13 , Issue 6 , November 1995 , pp. 599 - 606
Copyright
Copyright © Cambridge University Press 1995

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