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The power dissipation method and kinematic reducibility of multiple-model robotic systems

Murphey, Todd D. and Burdick, Joel W. (2006) The power dissipation method and kinematic reducibility of multiple-model robotic systems. IEEE Transactions on Robotics, 22 (4). pp. 694-710. ISSN 1552-3098. https://resolver.caltech.edu/CaltechAUTHORS:MURieeetr06

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Abstract

This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems.


Item Type:Article
Additional Information:© 2006 IEEE. Reprinted with permission. Manuscript received November 7, 2004; revised July 22, 2005. [Posted online: 2006-08-07] This paper was recommended for publication by Associate Editor D. Prattichizzo and Editor H. Arai upon evaluation of the reviewers’ comments. This work was supported in part by the National Science Foundation under Grant NSF9402726 through its Engineering Research Center (ERC) program. This paper was presented in part at the International Conference on Robotics and Automation, Seoul, South Korea, 2001, and in part at the Conference on Decision and Control, Maui, HI, 2003.
Funders:
Funding AgencyGrant Number
NSFEEC-9402726
Subject Keywords:Contact modeling, dynamics, frictional contacts, kinematic analysis, modeling for control
Issue or Number:4
Record Number:CaltechAUTHORS:MURieeetr06
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:MURieeetr06
Alternative URL:http://dx.doi.org/10.1109/TRO.2006.878971
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6354
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:04 Dec 2006
Last Modified:02 Oct 2019 23:31

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