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Model Predictive Control for Dynamic Walking

Duration: 65 min · Level: Advanced · Module: 3. Bipedal Locomotion & Whole-Body Control · Focus: MPC, locomotion, optimization, control

Learning objectives

By the end of this lesson you will be able to explain and apply:

  • MPC formulation
  • Contact-implicit MPC
  • MIT Cheetah 3 (2018)
  • Humanoid MPC
  • Centroidal MPC

Why this matters​

Model Predictive Control (MPC) replaced ZMP as the dominant approach for dynamic locomotion.

Overview​

Model Predictive Control (MPC) replaced ZMP as the dominant approach for dynamic locomotion. MPC plans a finite horizon of future states, solves an optimization at every control step, and handles contact transitions explicitly. It enables running, stair climbing, and perturbation recovery that ZMP controllers cannot achieve.

Key concepts​

Key idea

MPC formulation: minimize cost over horizon N while satisfying dynamics constraints, friction cone constraints, and joint limits; solve at 100-1000 Hz

  • Contact-implicit MPC: treats contact schedule (which foot contacts the ground when) as an optimization variable — can automatically discover new gaits
  • MIT Cheetah 3 (2018): used convex MPC at 500 Hz to achieve stable 3D running at 6 m/s with real-time re-planning on rough terrain
  • Humanoid MPC: more complex than quadruped — 40+ joints, whole-body inertial properties, upper-body dynamics couple to leg control
  • Centroidal MPC: reduce humanoid to centroidal dynamics (6 DOF center of mass) for planning; send outputs to whole-body QP controller for full joint commands
  • Key software: Drake (MIT), CROCODDYL (LAAS), PINOCCHIO (LAAS) — open-source libraries for humanoid MPC with sub-millisecond solve times

Check your understanding​

Try to recall each answer before expanding it.

Q1. What do you know about MPC formulation?

minimize cost over horizon N while satisfying dynamics constraints, friction cone constraints, and joint limits; solve at 100-1000 Hz

Q2. What do you know about Contact-implicit MPC?

treats contact schedule (which foot contacts the ground when) as an optimization variable — can automatically discover new gaits

Q3. What do you know about MIT Cheetah 3 (2018)?

used convex MPC at 500 Hz to achieve stable 3D running at 6 m/s with real-time re-planning on rough terrain

Q4. What do you know about Humanoid MPC?

more complex than quadruped — 40+ joints, whole-body inertial properties, upper-body dynamics couple to leg control

Q5. What do you know about Centroidal MPC?

reduce humanoid to centroidal dynamics (6 DOF center of mass) for planning; send outputs to whole-body QP controller for full joint commands

References​

  • Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control — Di Carlo et al. (2018). IROS 2018
  • Centroidal Dynamics of a Humanoid Robot — Orin et al. (2013). Autonomous Robots

← Previous: 3.1 Locomotion Foundations: ZMP, CoM, and Linear Inverted Pendulum · Next: 3.3 Reinforcement Learning for Locomotion →

Part of Module 3: Bipedal Locomotion & Whole-Body Control.