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Analysis of a Simplified Hopping Robot

International Journal of Robotics Research, December 1991

D. E. Koditschek and Martin Buehler
Yale University
Full PDF | Penn ScholarlyCommons | Web Link

Abstract
This article offers some analytical results concerning simplified models of Raibert’s hopper. We represent the task of achieving a recurring hopping height for an actuated “ball” robot as a stability problem in a nonlinear discrete dynamical control system. We model the properties of Raibert’s control scheme in a simplified fashion and argue that his strategy leads to closed-loop dynamics governed by a well-known class of functions, the unimodal maps. The rich mathematical literature on this subject greatly advances our ability to determine the presence of an essentially globally attracting fixed point—the formal rendering of what we intuitively mean by a “correct” strategy. The motivation for this work is the hope that it will facilitate the development of general design principles for “dynamically dexterous” robots.
BibTeX entry
@article{ koditschek-ijrr-1991,
  author = {D.E. Koditschek and M. Buehler},
  title = {Analysis of a Simplified Hopping Robot},
  journal ={International Journal of Robotics Research},
  volume = {10},
  number = {6},
  year = {1991},
  pages = {587-605},
}

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