Stable Walking for Bipedal Locomotion under Foot-Slip via Virtual Nonholonomic Constraints

TL;DR

This paper introduces a control framework for bipedal walking that explicitly manages foot slip using virtual nonholonomic constraints, enhancing stability on low-friction terrains.

Contribution

It develops a hybrid dynamical system approach with nonlinear feedback to enforce slip-compatible constraints, improving walking stability under slip conditions.

Findings

Stability of walking gaits is achieved despite foot slip.

The control framework effectively regulates tangential foot velocity.

Numerical simulations demonstrate successful stabilization under slip.

Abstract

Foot slip is a major source of instability in bipedal locomotion on low-friction or uncertain terrain. Standard control approaches typically assume no-slip contact and therefore degrade when slip occurs. We propose a control framework that explicitly incorporates slip into the locomotion model through virtual nonholonomic constraints, which regulate the tangential stance-foot velocity while remaining compatible with the virtual holonomic constraints used to generate the walking gait. The resulting closed-loop system is formulated as a hybrid dynamical system with continuous swing dynamics and discrete impact events. A nonlinear feedback law enforces both classes of constraints and yields a slip-compatible hybrid zero dynamics manifold for the reduced-order locomotion dynamics. Stability of periodic walking gaits is characterized through the associated Poincar\'e map, and numerical results illustrate stabilization under slip conditions.