Chaotic motions in the dynamics of a hopping robot

Alexander F Vakakis, J. W. Burdick

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Discrete dynamical systems theory is applied to the dynamic stability analysis of a simplified hopping robot. A Poincarereturn map is developed to capture the system dynamic behavior, and two basic nondimensional parameters which influence the systems dynamics are identified. The hopping behavior of the system is investigated by constructing the bifurcation diagrams of the Poincarereturn map with respect to these parameters. The bifurcation diagrams show a period-doubling cascade leading to a regime of chaotic behavior, where a strange attractor is developed. One 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 hopping thrust. Physically, the collapse of the strange attractor leads to globally stable uniform hopping motion.

Original languageEnglish (US)
Title of host publicationProc 1990 IEEE Int Conf Rob Autom
PublisherPubl by IEEE
Number of pages6
ISBN (Print)0818620617
StatePublished - 1990
Externally publishedYes
EventProceedings of the 1990 IEEE International Conference on Robotics and Automation - Cincinnati, OH, USA
Duration: May 13 1990May 18 1990


OtherProceedings of the 1990 IEEE International Conference on Robotics and Automation
CityCincinnati, OH, USA

ASJC Scopus subject areas

  • Engineering(all)


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