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Adaptive and Singularity-Free Inverse Dynamics Models for Control of Parallel Manipulators With Actuation Redundancy

[+] Author Affiliations
Andreas Müller

University Duisburg-Essen, Duisburg, Germany

Timo Hufnagel

Heilbronn University, Heilbronn, Germany

Paper No. DETC2011-47943, pp. 989-997; 9 pages
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5483-9
  • Copyright © 2011 by ASME


Redundant actuation of parallel kinematics machines (PKM) is a way to eliminate input-singularities and so to enlarge the usable workspace. From a kinematic point of view the number m of actuator coordinates exceeds the DOF δ of a redundantly actuated PKM (RA-PKM). The dynamics model, being the basis for model-based control, is usually expressed in terms of δ independent actuator coordinates. This implies that the model exhibits the same singularities as the non-redundant PKM, even though the RA-PKM is not singular. Consequently the admissible range of motion of the RA-PKM model is limited to that of the non-redundant PKM. In this paper an alternative formulation of the dynamics model in terms of the full set of m actuator coordinates is presented. It leads to a redundant system of m motion equations that is valid in the entire range of motion. This formulation gives rise to an inverse dynamics formulation tailored for real-time implementation. In contrast to the standard formulation in independent coordinates, the proposed inverse dynamics formulation does not involve control forces in the null space of the control matrix, i.e. it does not allow for the generation of internal prestresses, however. This is not problematic as the latter is usually not exploited. The proposed method is compared to the recently proposed adaptive coordinate switching method. Experimental results are reported if the inverse dynamics solution is introduced in model-based computed torque control scheme of a planar 2DOF RA-PKM.

Copyright © 2011 by ASME



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