Multi-contact Stability: Support Areas and Volumes for Humanoid Locomotion under Frictional Contacts

Humanoid locomotion on horizontal floors was solved by closing the feedback loop on the Zero-tiling Moment Point (ZMP), a measurable dynamic point that needs to stay inside the foot contact area to prevent the robot from falling (contact stability criterion). However, this criterion does not apply to general multi-contact settings, the "new frontier" in humanoid locomotion. In this talk, we will see how the ideas of ZMP and support area can be generalized and applied to multi-contact locomotion. First, we will show how support areas can be calculated in any virtual plane, allowing one to apply classical schemes even when contacts are not coplanar. Yet, these schemes constraint the center-of-mass (COM) to planar motions. We overcome this limitation by extending the calculation of the contact-stability criterion from a support area to a support cone of 3D COM accelerations. We use this new criterion to implement a multi-contact walking pattern generator based on predictive control of COM accelerations, which we will demonstrate in real-time simulations during the presentation.