ZMP support areas for multi-contact mobility under frictional constraints

TL;DR

This paper extends the concept of ZMP support areas to multi-contact scenarios with frictional constraints, providing new geometric tools and algorithms for ensuring humanoid robot stability in complex environments.

Contribution

It introduces generalized ZMP support areas considering friction and multiple contacts, and develops algorithms for computing these areas under different constraints.

Findings

The full support area can be geometrically constructed for valid contact forces.

The pendular support area shrinks under Linear Pendulum Mode constraints.

ZMP within the pendular support area guarantees contact stability.

Abstract

We propose a method for checking and enforcing multi-contact stability based on the Zero-tilting Moment Point (ZMP). The key to our development is the generalization of ZMP support areas to take into account (a) frictional constraints and (b) multiple non-coplanar contacts. We introduce and investigate two kinds of ZMP support areas. First, we characterize and provide a fast geometric construction for the support area generated by valid contact forces, with no other constraint on the robot motion. We call this set the full support area. Next, we consider the control of humanoid robots using the Linear Pendulum Mode (LPM). We observe that the constraints stemming from the LPM induce a shrinking of the support area, even for walking on horizontal floors. We propose an algorithm to compute the new area, which we call pendular support area. We show that, in the LPM, having the ZMP in the pendular support area is a necessary and sufficient condition for contact stability. Based on these developments, we implement a whole-body controller and generate feasible multi-contact motions where an HRP-4 humanoid locomotes in challenging multi-contact scenarios.