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On the Boundedness Property of the Inertia Matrix and Skew-Symmetric Property of the Coriolis Matrix for Vehicle-Manipulator Systems

[+] Author and Article Information
Pål Johan From

 Department Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås 1432, Norwaypafr@umb.no

Ingrid Schjølberg

 Applied Cybernetics, SINTEF, Trondheim, Norway

Jan Tommy Gravdahl, Kristin Ytterstad Pettersen, Thor I. Fossen

 Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway

J. Dyn. Sys., Meas., Control 134(4), 044501 (Apr 27, 2012) (4 pages) doi:10.1115/1.4006077 History: Received September 17, 2010; Revised November 19, 2011; Published April 26, 2012; Online April 27, 2012

This paper addresses the boundedness property of the inertia matrix and the skew-symmetric property of the Coriolis matrix for vehicle-manipulator systems. These properties are widely used in control theory and Lyapunov-based stability proofs and thus important to identify. The skew-symmetric property does not depend on the system at hand but on the parameterization of the Coriolis matrix, which is not unique. It is the authors’ experience that many researchers take this assumption for granted without taking into account that several parameterizations exist. In fact, most researchers refer to references that do not show this property for vehicle-manipulator systems but for other systems such as single rigid bodies or fixed-base manipulators. As a result, the otherwise rigorous stability proofs fall apart. In this paper, we list some relevant references and give the correct proofs for some commonly used parameterizations for future reference. Depending on the choice of state variables, the boundedness of the inertia matrix will not necessarily hold. We show that deriving the dynamics in terms of quasi-velocities leads to an inertia matrix that is bounded in its variables. To the best of our knowledge, we derive for the first time the dynamic equations of vehicle-manipulator systems with non-Euclidean joints for which both properties are true.

Copyright © 2012 by American Society of Mechanical Engineers
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