Planar bipedal jumping gaits with stable landing

Dip Goswami, Prahlad Vadakkepat

Research output: Contribution to journalArticleAcademicpeer-review

28 Citations (Scopus)


In this paper, landing stability of jumping gaits is studied for a four-link planar biped model. Rotation of the foot during the landing phase leads to underactuation due to the passive degree of freedom at the toe, which results in nontrivial zero dynamics (ZD). Compliance between the foot and ground is modeled as a spring-damper system. Rotation of the foot along with the compliance model introduces switching in the ZD. The stability conditions for the "switching ZD" and closed-loop dynamics (CLD) are established. " Critical potential index" and "critical kinetic index" are introduced as measures of the stability of the CLD of the biped during landing. Landing stability is achieved by utilizing the stability conditions. Stable jumping motion is experimentally realized on a biped robot.

Original languageEnglish
Article number5173532
Pages (from-to)1030-1046
Number of pages17
JournalIEEE Transactions on Robotics
Issue number5
Publication statusPublished - 28 Jul 2009
Externally publishedYes


  • Biped robot
  • Closed-loop dynamics (CLD)
  • Critical potential index and critical kinetic index
  • Jumping gaits
  • Landing stability
  • Multiple Lyapunov function (MLF)
  • Singular perturbation
  • Switching zero dynamics (ZD)


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