Learning and Generalization of Compensative Zero-Moment Point Trajectory for Biped Walking

Kai Hu, Christian Ott, Dongheui Lee

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


This paper presents an online learning framework for improving the robustness of zero-moment point (ZMP)-based biped walking controllers. The key idea is to learn a feedforward compensative ZMP (CZMP) trajectory from measured ZMP errors during repetitive walking motions by applying iterative learning control theory. The learned CZMP trajectory adjusts the reference ZMP and reduces the effect of unmodeled dynamics at the pattern-generation stage. From individual learned CZMP trajectories of typical walking parameters, we can build up a CZMP database. This database can be used for generating an initial CZMP whenever a new walking pattern is executed. A prediction from the database is done by k-nearest neighbor regression based on the Mahalonobis distance. Compared with state-of-the-art model-based methods, the proposed learning approach is model free and allows online adaptation to constant unknown disturbances. Enhanced walking robustness can be observed from reduced average ZMP error and more robust reaction against external disturbances on the DLR humanoid robot TORO.

Original languageEnglish
Article number7484896
Pages (from-to)717-725
Number of pages9
JournalIEEE Transactions on Robotics
Issue number3
StatePublished - Jun 2016
Externally publishedYes


  • Balance control
  • biped walking control
  • iterative learning control (ILC)


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