Modeling and control of legged locomotion

Abstract¶

The objective of this lecture is to understand the physics of balancing and how we can leverage them to design locomotion controllers.

Content¶

Slides

Simulation¶

On Linux, formerly we could run the humanoid walking controller in a simulator with the following command. It is the software that run in the real-robot experiments at the Airbus Saint-Nazaire factory in February 2019.

$ xhost + # for X11 forwarding
$ docker run -it --rm --user ayumi -e DISPLAY=${DISPLAY} \
    -v /tmp/.X11-unix:/tmp/.X11-unix:rw \
    stephanecaron/lipm_walking_controller \
    lipm_walking --staircase

Update: Unfortunately the Docker Hub took down the image some time in 2025. Feel free to reach out if you are interested in running the image locally on your machine.

References¶

Modeling¶

	Forces Acting on a Biped Robot. Center of Pressure—Zero Moment Point
	Stability of Surface Contacts for Humanoid Robots: Closed-Form Formulae of the Contact Wrench Cone for Rectangular Support Areas
	The 3D Linear Inverted Pendulum Mode: A simple modeling for a biped walking pattern generation
	ZMP support areas for multi-contact mobility under frictional constraints

Model predictive control¶

	Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control
	Model preview control in multi-contact motion-application to a humanoid robot
	Trajectory Free Linear Model Predictive Control for Stable Walking in the Presence of Strong Perturbations

Balance control¶

	Biped Walking Stabilization Based on Linear Inverted Pendulum Tracking
	Stair Climbing Stabilization of the HRP-4 Humanoid Robot using Whole-body Admittance Control

Lectures¶

This lecture was given in the following courses:

• Fall 2025 class at École normale supérieure, Paris.
• Fall 2024 class at École normale supérieure, Paris.
• Fall 2024 class (snapshot) at Master MVA, Paris.
• Fall 2023 class at École normale supérieure, Paris.