Rate of angular momentum in ZMP using efficient DH-based recursive lagrangian

Hyun Joon Chung, Joo H. Kim, Yujiang Xiang

Research output: Contribution to journalArticlepeer-review


Dynamic balance has to be maintained during motions of biped systems when their feet are in contact with the ground. As a necessary condition, this indicates that the calculated zero moment point (ZMP) position should be within the specified foot support region throughout the entire motion. A critical term in the ZMP formulation is the rate of angular momentum (RAM) for each link, which should be evaluated accurately and efficiently in motion planning and simulations. In this study, we propose a recursive Lagrangian method based on Denavit-Hartenberg convention to calculate the RAM for each link and the corresponding sensitivity. This method allows the evaluation of each link's dynamic contribution to the ZMP position. The effectiveness of the proposed approach is demonstrated by simulating bipedal motions of walking and running along with their comparison against existing approaches (direct method and global force method). The accurate RAM calculation in ZMP based on the proposed approach resulted in the improved motion trajectories and reliable ground reaction forces for high-speed bipedal motion predictions.

Original languageEnglish (US)
Article number1850028
JournalInternational Journal of Humanoid Robotics
Issue number6
StatePublished - Dec 1 2018


  • Zero moment point (ZMP)
  • motion planning
  • rate of angular momentum (RAM)
  • recursive Lagrangian method
  • running
  • walking

ASJC Scopus subject areas

  • Mechanical Engineering
  • Artificial Intelligence


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