Towards the Geometric Reduction of Controlled Three-Dimensional Robotic Bipedal Walkers
A. Ames, R. Gregg, E.D.B. Wendel, S. Sastry

Citation
A. Ames, R. Gregg, E.D.B. Wendel, S. Sastry. "Towards the Geometric Reduction of Controlled Three-Dimensional Robotic Bipedal Walkers". Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, July, 2006.

Abstract
The purpose of this paper is to apply methods from geometric mechanics to the analysis and control of robotic bipedal 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 for a three-dimensional bipedal walker that provably results in walking gaits on flat ground.

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• HTML

  A. Ames, R. Gregg, E.D.B. Wendel, S. Sastry. <a
  href="http://chess.eecs.berkeley.edu/pubs/127.html"
  >Towards the Geometric Reduction of Controlled
  Three-Dimensional Robotic Bipedal Walkers</a>,
  Workshop on Lagrangian and Hamiltonian Methods for Nonlinear
  Control, July, 2006.

• Plain text

  A. Ames, R. Gregg, E.D.B. Wendel, S. Sastry. "Towards
  the Geometric Reduction of Controlled Three-Dimensional
  Robotic Bipedal Walkers". Workshop on Lagrangian and
  Hamiltonian Methods for Nonlinear Control, July, 2006.

• BibTeX

  @inproceedings{AmesGreggWendelSastry06_TowardsGeometricReductionOfControlledThreeDimensional,
      author = {A. Ames and R. Gregg and E.D.B. Wendel and S.
                Sastry},
      title = {Towards the Geometric Reduction of Controlled
                Three-Dimensional Robotic Bipedal Walkers},
      booktitle = {Workshop on Lagrangian and Hamiltonian Methods for
                Nonlinear Control},
      month = {July},
      year = {2006},
      abstract = {The purpose of this paper is to apply methods from
                geometric mechanics to the analysis and control of
                robotic bipedal 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 for a
                three-dimensional bipedal walker that provably
                results in walking gaits on flat ground.},
      URL = {http://chess.eecs.berkeley.edu/pubs/127.html}
  }
  

Posted by Aaron Ames on 15 May 2006.
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