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Random Matrix Based Input Shaping Control of Uncertain Parallel Manipulators

[+] Author Affiliations
Javad Sovizi, Aliakbar Alamdari, Madusudanan Sathia Narayanan, Venkat Krovi

University at Buffalo, Buffalo, NY

Paper No. DETC2014-34451, pp. V007T05A008; 10 pages
doi:10.1115/DETC2014-34451
From:
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 7: 2nd Biennial International Conference on Dynamics for Design; 26th International Conference on Design Theory and Methodology
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4640-7
  • Copyright © 2014 by ASME

abstract

Input shaping control techniques have proven to be very effective in improving performance and lowering actuation requirements for Linear Time-Invariant (LTI) systems. However, deployments tend to be very sensitive to variation of the system natural frequencies and damping ratios. This limits the application of input shaping schemes in the nonlinear systems (e.g., robotic manipulators) or systems with uncertain parameters. The main focus of this paper is to address the parametric uncertainty in the system and the design of an input shaping control based upon the estimated parameters. The variations induced by system non-linearity are tackled by the method of the linearization. The uncertainty is characterized by treating the linearized system mass matrix as a random matrix. This provides the probability density function of the eigenvalues of the underdamped system that are then used to design the input shaping control for the uncertain system. We believe that such a characterization (and desensitization to production variability) is especially important for successful deployment of newer generations of 3D printed robotic systems. This is verified via a Monte Carlo simulation — the statistics of the percent residual vibration verifies the superiority of the input shaping control scheme based on the estimated parameter values (compared to the one based on the nominal parameters).

Copyright © 2014 by ASME
Topics: Manipulators

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