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

  • Aaron D. Ames
  • Robert D. Gregg
  • Eric D.B. Wendel
  • Shankar Sastry
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 366)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Aaron D. Ames
    • 1
  • Robert D. Gregg
    • 2
  • Eric D.B. Wendel
    • 3
  • Shankar Sastry
    • 4
  1. 1.Control and Dynamical SystemsCalifornia Institute of TechnologyPasadena
  2. 2.Department of Electrical and Computer EngineeringUniversity of Illinois at Urbana-ChampaignUrbana
  3. 3.Sensis CorporationCampbell
  4. 4.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeley

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