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A Proposal for a Unified Concept of Kinematic Singularities for Holonomic and Non-Holonomic Mechanisms

[+] Author Affiliations
Andreas Müller

Institute of Mechatronics, Chemnitz, Germany

Paper No. DETC2012-70649, pp. 1543-1552; 10 pages
doi:10.1115/DETC2012-70649
From:
  • ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B
  • Chicago, Illinois, USA, August 12–15, 2012
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4503-5
  • Copyright © 2012 by ASME

abstract

The study of mechanism singularities has traditionally focused on holonomic systems. On the other hand many robotic systems are characterized by non-holonomic constraints, such as mobile platforms and manipulators driven by non-holonomic joints, and a general concept of singularities seems in order. In this paper a possible generalization of the singularity concept is proposed that equally accounts for holonomic and non-holonomic kinematic systems. The central object is the associated kinematic control problem. Singularities are identified as those configurations where the iteration depth of Lie brackets required to compute the accessibility Lie algebra changes. This notion of singularities is applied to serial manipulator and to non-holonomic mobile platforms. It is shown for holonomic manipulators that this is equivalent to the usual Jacobian rank condition. As example the condition is discussed for a Scara manipulator, a 6R manipulator, and for a kinematic car with one or two trailers.

Copyright © 2012 by ASME
Topics: Kinematics

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