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On the Geometric Reduction of Controlled Three-Dimensional Bipedal Robotic Walkers

Ames, Aaron D. and Gregg, Robert D. and Wendel, Eric D. B. and Sastry, Shankar (2007) On the Geometric Reduction of Controlled Three-Dimensional Bipedal Robotic Walkers. In: Lagrangian and Hamiltonian Methods for Nonlinear Control 2006. Lecture Notes in Control and Information Sciences. No.366. Springer , Berlin, pp. 183-196. ISBN 978-3-540-73889-3.

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The purpose of this paper is to apply methods from geometric mechanics to the analysis and control of bipedal robotic walkers. We begin by introducing a generalization of Routhian reduction, functional Routhian Reduction, which allows for the conserved quantities to be functions of the cyclic variables rather than constants. Since bipedal robotic walkers are naturally modeled as hybrid systems, which are inherently nonsmooth, in order to apply this framework to these systems it is necessary to first extend functional Routhian reduction to a hybrid setting. We apply this extension, along with potential shaping and controlled symmetries, to derive a feedback control law that provably results in walking gaits on flat ground for a three-dimensional bipedal walker given walking gaits in two dimensions.

Item Type:Book Section
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URLURL TypeDescription ReadCube access
Ames, Aaron D.0000-0003-0848-3177
Gregg, Robert D.0000-0002-0729-2857
Additional Information:© 2007 Springer-Verlag Berlin Heidelberg.
Series Name:Lecture Notes in Control and Information Sciences
Issue or Number:366
Record Number:CaltechAUTHORS:20100819-102549602
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19507
Deposited By: Tony Diaz
Deposited On:19 Aug 2010 22:37
Last Modified:08 Nov 2021 23:53

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