An “Interesting” Strange Attractor in the Dynamics of a Hopping Robot

A. F. Vakakis, J. W. Burdick, T. K. Caughey

Research output: Contribution to journalArticlepeer-review


This article applies discrete dynamical systems theory to the dynamic analysis of a simplified vertical hopping robot model that is analogous to Raibert's hopping machines. A Poincaré return map is developed to capture the dynamic behavior, and two basic nondimensional parameters that influence the systems dynamics are iden tified. The hopping behavior of the system is investigated by constructing the bifurcation diagrams of the Poincaré return map. The bifurcation diagrams show a period-dou bling cascade leading to a regime of chaotic behavior, where a “strange attractor” is developed. An interesting feature of the dynamics is that the strange attractor can be controlled and eliminated by tuning an appropriate parameter corresponding to the duration of applied hop ping thrust. Physically, the collapse of the strange attrac tor leads to a globally stable period-1 orbit, which guar antees a stable uniform hopping motion.

Original languageEnglish (US)
Pages (from-to)606-618
Number of pages13
JournalThe International Journal of Robotics Research
Issue number6
StatePublished - Dec 1991
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Mechanical Engineering
  • Artificial Intelligence
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Modeling and Simulation


Dive into the research topics of 'An “Interesting” Strange Attractor in the Dynamics of a Hopping Robot'. Together they form a unique fingerprint.

Cite this