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Journal of Computational and Nonlinear Dynamics | Volume 4 | Issue 3 | Research Paper
Research Papers

A Gauge-Invariant Formulation for Constrained Mechanical Systems Using Square-Root Factorization and Unitary Transformation

[+] Author and Article Information
Farhad Aghili

Space Technologies, Canadian Space Agency, Saint-Hubert, QC J3Y 8Y9 Canadafarhad.aghili@space.gc.ca

A manifold with a Euclidean metric is said to be “flat” and the curvature associated with it is identically zero (11).

Also known as generalized coordinates.

By definition, a Riemannian manifold that is locally isometric to Euclidean manifold is called a locally flat manifold (9).

J. Comput. Nonlinear Dynam 4(3), 031010 (Jun 09, 2009) (10 pages) doi:10.1115/1.3124094 History: Received May 01, 2008; Revised January 13, 2009; Published June 09, 2009
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A gauge-invariant formulation for deriving the dynamic equations of constrained multibody systems in terms of (reduced) quasivelocities is presented. This formulation does not require any weighting matrix to deal with the gauge-invariance problem when both translational and rotational components are involved in the generalized coordinates or in the constraint equations. Moreover, in this formulation the equations of motion are decoupled from those of constrained force, and each system has its own independent input. This allows the possibility to develop a simple force control action that is totally independent from the motion control action facilitating a hybrid force/motion control. Tracking force/motion control of constrained multibody systems based on a combination of feedbacks on the vectors of the quasivelocities and the configuration-variables are presented.
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Copyright © 2009 by the Canadian Government
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+Cart pole system
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Cart pole system
Figure 1

Cart pole system

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+Constrained motion of a Cartesian manipulator
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Constrained motion of a Cartesian manipulator
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Constrained motion of a Cartesian manipulator

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+Simulated position and force responses
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Simulated position and force responses
Figure 3

Simulated position and force responses

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+A constrained PRR manipulator
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A constrained PRR manipulator
Figure 4

A constrained PRR manipulator

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+Simulated motion tracking
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Simulated motion tracking
Figure 5

Simulated motion tracking

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+Simulated constrained force
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Simulated constrained force
Figure 6

Simulated constrained force

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+Trajectories of the quasiforces
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Trajectories of the quasiforces
Figure 7

Trajectories of the quasiforces

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