Passive and dynamic gait measures for biped mechanism: Formulation and simulation analysis

Carlotta Mummolo, Joo H. Kim

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


Understanding and mimicking human gait is essential for design and control of biped walking robots. The unique characteristics of normal human gait are described as passive dynamic walking, whereas general human gait is neither completely passive nor always dynamic. To study various walking motions, it is important to quantify the different levels of passivity and dynamicity, which have not been addressed in the current literature. In this paper, we introduce the initial formulations of Passive Gait Measure (PGM) and Dynamic Gait Measure (DGM) that quantify passivity and dynamicity, respectively, of a given biped walking motion, and the proposed formulations will be demonstrated for proof-of-concepts using gait simulation and analysis. The PGM is associated with the optimality of natural human walking, where the passivity weight functions are proposed and incorporated in the minimization of physiologically inspired weighted actuator torques. The PGM then measures the relative contribution of the stance ankle actuation. The DGM is associated with the gait stability, and quantifies the effects of inertia in terms of the Zero-Moment Point and the ground projection of center of mass. In addition, the DGM takes into account the stance foot dimension and the relative threshold between static and dynamic walking. As examples, both human-like and robotic walking motions during single support phase are generated for a planar biped system using the passivity weights and proper gait parameters. The calculated PGM values show more passive nature of human-like walking as compared with the robotic walking. The DGM results verify the dynamic nature of normal human walking with anthropomorphic foot dimension. In general, the DGMs for human-like walking are greater than those for robotic walking. The resulting DGMs also demonstrate their dependence on the stance foot dimension as well as the walking motion; for a given walking motion, smaller foot dimension results in increased dynamicity. Future work on experimental validation and demonstration will involve actual walking robots and human subjects. The proposed results will benefit the human gait studies and the development of walking robots.

Original languageEnglish (US)
Pages (from-to)555-572
Number of pages18
Issue number4
StatePublished - Jul 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Software
  • General Mathematics
  • Computer Science Applications


  • Biped system
  • Dynamic gait measure (DGM)
  • Optimization
  • Passive dynamic walking
  • Passive gait measure (PGM)
  • Passivity weight
  • Stability
  • Static walking
  • Zero-moment point (ZMP)


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