Stable Walking for Bipedal Locomotion under Foot-Slip via Virtual Nonholonomic Constraints
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.
Cite
@article{arxiv.2603.29050,
title = {Stable Walking for Bipedal Locomotion under Foot-Slip via Virtual Nonholonomic Constraints},
author = {Leonardo Colombo and Álvaro Rodríguez Abella and Alexandre Anahory Simoes and Anthony Bloch},
journal= {arXiv preprint arXiv:2603.29050},
year = {2026}
}