Variable Horizon MPC with Swing Foot Dynamics for Bipedal Walking Control

Elham Daneshmand, Majid Khadiv, Felix Grimminger, Ludovic Righetti

Research output: Contribution to journalArticlepeer-review


In this letter, we present a novel two-level variable Horizon Model Predictive Control (VH-MPC) framework for bipedal locomotion. In this framework, the higher level computes the landing location and timing (horizon length) of the swing foot to stabilize the unstable part of the center of mass (CoM) dynamics, using feedback from the CoM states. The lower level takes into account the swing foot dynamics and generates dynamically consistent trajectories for landing at the desired time as close as possible to the desired location. To do that, we use a simplified model of the robot dynamics projected in swing foot space that takes into account joint torque constraints as well as the friction cone constraints of the stance foot. We show the effectiveness of our proposed control framework by implementing robust walking patterns on our torque-controlled and open-source biped robot, Bolt. We report extensive simulations and real robot experiments in the presence of various disturbances and uncertainties.

Original languageEnglish (US)
Article number9361296
Pages (from-to)2349-2356
Number of pages8
JournalIEEE Robotics and Automation Letters
Issue number2
StatePublished - Apr 2021


  • Humanoid and bipedal locomotion
  • legged robots
  • motion control
  • optimization and optimal control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Biomedical Engineering
  • Human-Computer Interaction
  • Mechanical Engineering
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Control and Optimization
  • Artificial Intelligence


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