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RoManSy 6 pp 120-127 | Cite as

Invariant Kinestatic Filtering

  • H. Lipkin
  • J. Duffy

Abstract

Three necessary conditions derived from classical geometry are proposed to evaluate formulations for the simultaneous twist and wrench control of rigid bodies, and for any theory to be meaningful it must be invariant with respect to (1) Euclidean Collineations, (2) Change of Unit Length, and (3) Change of Basis. It is demonstrated in this paper that a previously established theory of hybrid control for robot manipulators (see for example [1–3]) is in fact based on noninvariant principles and is noninvariant with respect to (1) and (2). A new alternative invariant formulation based on screw theory is presented. An example of insertion is included which illustrates both invariant and noninvariant methods.

Keywords

Virtual Work Robotic Manipulator Hybrid Control Projective Relation Screw Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Lipkin, H., “Geometry and Mappings of Screws with Applications to the Hybrid Control of Robotic Manipulators,” Ph.D. Dissertation, Univ. of Florida, 1985.Google Scholar
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    Lipkin, H. and Duffy, J., “On the Geometry of Orthogonal and Reciprocal Screws,” Theory and Practice of Robots and Manipulators, Proc. RoManSy’84: 5th CISMIFToMM Sym., A. Morecki, et al. Eds., Udine, 1984, pp. 47–56.Google Scholar
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    Lipkin, H. and Duffy, J., “The Elliptic Polarity of Screws,” ASME J. of Mech., Trans. and Auto. in Design, vol. 107, Sept. 1985, pp. 377–387.CrossRefGoogle Scholar
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    Porteous, I.R., Topological Geometry, 2nd Edition, Cambridge Univ. Press, 1981.CrossRefGoogle Scholar

Copyright information

© Hermes, Paris 1987

Authors and Affiliations

  • H. Lipkin
    • 1
  • J. Duffy
    • 2
  1. 1.The George W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Center for Intelligent MachinesRobotics University of FloridaGainesvilleUSA

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