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.
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July 2012
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On the Boundedness Property of the Inertia Matrix and Skew-Symmetric Property of the Coriolis Matrix for Vehicle-Manipulator Systems Available to Purchase
Pål Johan From,
e-mail: [email protected]
Pål Johan From
Department Mathematical Sciences and Technology, Norwegian University of Life Sciences
, Ås 1432, Norway
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Ingrid Schjølberg,
Ingrid Schjølberg
Applied Cybernetics, SINTEF
, Trondheim, Norway
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Jan Tommy Gravdahl,
Jan Tommy Gravdahl
Department of Engineering Cybernetics, Norwegian University of Science and Technology
, Trondheim, Norway
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Kristin Ytterstad Pettersen,
Kristin Ytterstad Pettersen
Department of Engineering Cybernetics, Norwegian University of Science and Technology
, Trondheim, Norway
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Thor I. Fossen
Thor I. Fossen
Department of Engineering Cybernetics, Norwegian University of Science and Technology
, Trondheim, Norway
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Pål Johan From
Department Mathematical Sciences and Technology, Norwegian University of Life Sciences
, Ås 1432, Norway
e-mail: [email protected]
Ingrid Schjølberg
Applied Cybernetics, SINTEF
, Trondheim, Norway
Jan Tommy Gravdahl
Department of Engineering Cybernetics, Norwegian University of Science and Technology
, Trondheim, Norway
Kristin Ytterstad Pettersen
Department of Engineering Cybernetics, Norwegian University of Science and Technology
, Trondheim, Norway
Thor I. Fossen
Department of Engineering Cybernetics, Norwegian University of Science and Technology
, Trondheim, Norway
J. Dyn. Sys., Meas., Control. Jul 2012, 134(4): 044501 (4 pages)
Published Online: April 27, 2012
Article history
Received:
September 17, 2010
Revised:
November 19, 2011
Published:
April 26, 2012
Online:
April 27, 2012
Citation
Johan From, P., Schjølberg, I., Tommy Gravdahl, J., Ytterstad Pettersen, K., and Fossen, T. I. (April 27, 2012). "On the Boundedness Property of the Inertia Matrix and Skew-Symmetric Property of the Coriolis Matrix for Vehicle-Manipulator Systems." ASME. J. Dyn. Sys., Meas., Control. July 2012; 134(4): 044501. https://doi.org/10.1115/1.4006077
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