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

2026-03-30

AI Summary

This work addresses the instability of bipedal robots on low-friction or uncertain terrains caused by foot slippage. It introduces, for the first time, virtual nonholonomic constraints to explicitly model slipping behavior by modulating the tangential velocity of the stance foot, ensuring compatibility with the virtual holonomic constraints used in gait generation and thereby forming a closed-loop hybrid dynamical system. The approach establishes a slipping-compatible hybrid zero dynamics manifold and integrates nonlinear feedback control with Poincaré map-based stability analysis to guarantee robustness of periodic gaits. Numerical simulations demonstrate that the proposed method effectively maintains stable walking even under significant foot slippage, highlighting the novelty and efficacy of incorporating virtual nonholonomic constraints into bipedal gait control.

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 Poincaré map, and numerical results illustrate stabilization under slip conditions.

Problem

• bipedal locomotion
• foot slip
• stability
• low-friction terrain
• contact constraints

Innovation

• virtual nonholonomic constraints
• bipedal locomotion
• foot slip
• hybrid zero dynamics
• Poincaré map