Robust Locomotion Exploiting Multiple Balance Strategies: An Observer-Based Cascaded Model Predictive Control Approach

Jiatao Ding, Linyan Han, Ligang Ge, Yizhang Liu, Jianxin Pang

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
103 Downloads (Pure)


Robust locomotion is a challenging task for humanoid robots, especially when considering dynamic disturbances. This article proposes a disturbance observer-based cascaded model predictive control (MPC) approach for bipedal locomotion, with the capability of exploiting ankle, stepping, hip and height variation strategies. Specifically, based on the variable-height inverted pendulum model, a nonlinear MPC that is run at a low frequency is built for 3-D locomotion (i.e., with height variation) while accounting for the footstep modulation as well. Differing from previous works, the nonlinear MPC is formulated as a convex optimization problem by semidefinite relaxation. Subsequently, assuming a flywheel at the pelvis center, a linear MPC that is run at a high frequency is proposed to regulate angular momentum (e.g., through rotating the upper body), which is solved by convex quadratic programming. To run the cascaded MPC in a closed-loop manner, a high order sliding mode observer is designed to estimate system states and dynamic disturbances simultaneously. Simulation and hardware experiments demonstrate the walking robustness in real-world scenarios, including 3-D walking with varying speeds, walking across non-coplanar terrains and push recovery.

Original languageEnglish
Pages (from-to)2089-2097
JournalIEEE/ASME Transactions on Mechatronics
Issue number4
Publication statusPublished - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Bipedal locomotion
  • Computational modeling
  • convex optimization
  • disturbance observer
  • Foot
  • Hip
  • Legged locomotion
  • model predictive control
  • Predictive control
  • reactive walking
  • Solid modeling
  • Trajectory


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