Towards the Geometric Reduction of Controlled Three-Dimensional Bipedal Robotic Walkers
Aaron Ames, Robert Gregg, Eric D.B. Wendel, Shankar Sastry

Citation
Aaron Ames, Robert Gregg, Eric D.B. Wendel, Shankar Sastry. "Towards the Geometric Reduction of Controlled Three-Dimensional Bipedal Robotic Walkers". 3rd 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 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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• HTML

  Aaron Ames, Robert Gregg, Eric D.B. Wendel, Shankar Sastry.
  <a
  href="http://chess.eecs.berkeley.edu/pubs/260.html"
  >Towards the Geometric Reduction of Controlled
  Three-Dimensional Bipedal Robotic Walkers</a>, 3rd
  Workshop on Lagrangian and Hamiltonian Methods for Nonlinear
  Control, July, 2006.

• Plain text

  Aaron Ames, Robert Gregg, Eric D.B. Wendel, Shankar Sastry.
  "Towards the Geometric Reduction of Controlled
  Three-Dimensional Bipedal Robotic Walkers". 3rd
  Workshop on Lagrangian and Hamiltonian Methods for Nonlinear
  Control, July, 2006.

• BibTeX

  @inproceedings{AmesGreggWendelSastry06_TowardsGeometricReductionOfControlledThreeDimensional,
      author = {Aaron Ames and Robert Gregg and Eric D.B. Wendel
                and Shankar Sastry},
      title = {Towards the Geometric Reduction of Controlled
                Three-Dimensional Bipedal Robotic Walkers},
      booktitle = {3rd 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
                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.},
      URL = {http://chess.eecs.berkeley.edu/pubs/260.html}
  }
  

Posted by Aaron Ames on 16 May 2007.
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