Robust framework for the computed torque control of nondeterministic multibody dynamic systems

Sahand Sabet, Mohammad Poursina

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Considering uncertainty is inarguably a crucial aspect of dynamic analysis, design, and control of a mechanical system. When it comes to multibody problems, the effect of uncertainty in the system's parameters and excitations becomes even more significant due to the accumulation of inaccuracies. For this reason, this paper presents a detailed research on the use of the Polynomial Chaos Expansion (PCE) method for the control of nondeterministic multibody systems. PCE is essentially a way to compactly represent random variables. In this scheme, each stochastic response output and random input is projected onto the space of appropriate independent orthogonal polynomial basis functions. In the field of robotics, a required task is to force robotic arms to follow designated paths. Controlling such systems usually leads to difficulties since the dynamic equations of multibody problems are highly nonlinear. Computed Torque Control Law (CTCL) is able to overcome these difficulties by using feedback linearization to evaluate the required torque/force at any time to make the system follow a trajectory. In this paper, a mathematical framework is introduced to apply the Computed Torque Control Law to a multibody system with uncertainty. Surprisingly, it is shown that using this control scheme, uncertainty in geometry does not affect the closed-loop equations of controlled systems. Both the intrusive PCE method and the Monte Carlo approach are used to control a fully actuated two-link planar elbow arm where each link is required to follow a specified path. Lastly, a comparison of the time efficiency and accuracy between the traditionally used Monte Carlo method and the intrusive PCE is presented. The results indicate that the intrusive PCE approach can provide better accuracy with much less computation time than the Monte Carlo method.

Original languageEnglish (US)
Title of host publication12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers (ASME)
Volume6
ISBN (Electronic)9780791850183
DOIs
StatePublished - 2016
EventASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016 - Charlotte, United States
Duration: Aug 21 2016Aug 24 2016

Other

OtherASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016
CountryUnited States
CityCharlotte
Period8/21/168/24/16

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

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    Sabet, S., & Poursina, M. (2016). Robust framework for the computed torque control of nondeterministic multibody dynamic systems. In 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (Vol. 6). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC201660072