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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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References

1.Nakamura, Y., Advanced Robotics: Redundancy and Optimization (Addison-Wesley, Reading, Mass., 1991).Google Scholar
2.Baillieul, J., Hollerbach, J. and Brockett, R.W., “Programming and control of kinematically redundant manipulators” Proc. 23rd IEEE Conf. Decision and Control(1984) pp. 768–774.Google Scholar
3.Bedrossian, N.S., “Classification of singular configurations for redundant manipulators” Proc. IEEE Int. Conf. Robotics & Automat.(1990) pp. 818–823.Google Scholar
4.Bedrossian, N.S. and Flueckiger, K., “Characterizing spatial redundant manipulator singularities” Proc. IEEE Int. Conf. Robotics & Automat.(1991) pp. 714–719.Google Scholar
5.Shamir, T., “The singularities of redundant robot arm” Int. J. of Robotics Research 9(1), 113–121 (1990).Google Scholar
6.Tchori, K., “Differential topology of the inverse kinematic problem for redundant robot manipulators” Int. J. of Robotics Research 10(5), 492–504 (1991).Google Scholar
7.Tchoń, K. and Urban, P., “Classification of kinematic singularities in planar robot manipulators” Systems & Control Lett. 19, 293–302 (1992).Google Scholar
8.Burdick, J.W., “A classification of 3R regional manipulator singularities and geometries” Proc. IEEE Int. Conf. Robotics & Automat.(1991) pp. 2670–2675.Google Scholar
9.Spong, M.W. and Vidyasagar, M., Robot Dynamics and Control (J. Wiley, New York, 1989).Google Scholar
10.Tchoń, K. and Duleba, I., “Definition of a kinematic metric for robot manipoulators” J. Robotic Syst. 11(3), 211–222 (1994).Google Scholar
11.Park, F.C. and Brockett, R.W., “Kinematic dexterity of robotic mechanisms” Int. J. of Robotics Research 13(1), 1–15 (1994).Google Scholar
12.Abraham, R. and Marsden, J.E., Foundations of Mechanics (Benjamin, Reading, Mass., 1978).Google Scholar
13.Arnold, V.I., Mathematical Methods of Classical Mechanics (Nauka, Moscow, 1989) (in Russian).Google Scholar
14.Litvin, F.L. et al. , “Singularities in motion and displacement functions for a 7 degree-of-freedom manipulator” J. Robotic Syst. 4(3), 397–421 (1987).Google Scholar
15.Arnold, V.I. et al. , Singularities of Differentiate Maps (Birkhäuser, Boston, 1985).Google Scholar