Chapter

Lagrangian and Hamiltonian Methods for Nonlinear Control 2006

Volume 366 of the series Lecture Notes in Control and Information Sciences pp 183-196

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

  • Aaron D. AmesAffiliated withControl and Dynamical Systems, California Institute of Technology
  • , Robert D. GreggAffiliated withDepartment of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign
  • , Eric D.B. WendelAffiliated withSensis Corporation
  • , Shankar SastryAffiliated withDepartment of Electrical Engineering and Computer Sciences, University of California

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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.