All common bipedal gaits emerge from a single passive model

Zhenyu Gan, Yevgeniy Yesilevskiy, Petr Zaytsev, C. David Remy

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


In this paper, we systematically investigate passive gaits that emerge from the naturalmechanical dynamics of a bipedal system.We use an energetically conservative model of a simple spring-leg biped that exhibits well-defined swing leg dynamics. Through a targeted continuation of periodic motions of this model, we systematically identify different gaits that emerge from simple bouncing in place. We show that these gaits arise along one-dimensional manifolds that bifurcate into different branches with distinctly different motions. The branching is associated with repeated breaks in symmetry of the motion. Among others, the resulting passive dynamic gaits include walking, running, hopping, skipping and galloping. Our work establishes that the most common bipedal gaits can be obtained as different oscillatory motions (or nonlinear modes) of a single mechanical system with a single set of parameter values. For each of these gaits, the timing of swing leg motion and vertical motion is matched. This work thus supports the notion that different gaits are primarily a manifestation of the underlying natural mechanical dynamics of a legged system. Our results might explain the prevalence of certain gaits in nature, and may provide a blueprint for the design and control of energetically economical legged robots.

Original languageEnglish (US)
Article number0455
JournalJournal of the Royal Society Interface
Issue number146
StatePublished - Sep 1 2018
Externally publishedYes


  • bifurcations
  • bipedal gaits
  • passive dynamics

ASJC Scopus subject areas

  • Biotechnology
  • Biophysics
  • Bioengineering
  • Biomaterials
  • Biochemistry
  • Biomedical Engineering


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