On the Geometric Reduction of Controlled Three-Dimensional Bipedal Robotic Walkers
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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.
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- On the Geometric Reduction of Controlled Three-Dimensional Bipedal Robotic Walkers
- Book Title
- Lagrangian and Hamiltonian Methods for Nonlinear Control 2006
- Book Subtitle
- Proceedings from the 3rd IFAC Workshop, Nagoya, Japan, July 2006
- pp 183-196
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Control and Information Sciences
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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- Editor Affiliations
- 1. Mechanical Engineering Department, University of California at Santa Barbara
- 2. Department of Mechanical Science and Engineering, Nagoya University
- Author Affiliations
- 3. Control and Dynamical Systems, California Institute of Technology, Pasadena, CA, 91125
- 4. Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801
- 5. Sensis Corporation, Campbell, CA, 95008
- 6. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, 94720
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