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

• URL: http://arxiv.org/abs/2603.29050v1
• Date: Mon, 30 Mar 2026 22:38:45 GMT
• Title: Stable Walking for Bipedal Locomotion under Foot-Slip via Virtual Nonholonomic Constraints
• Abstract summary: Foot slip is a major source of instability in bipedal locomotion on low-friction or uncertain terrain.<n>We propose a control framework that explicitly incorporates slip into the locomotion model through virtual nonholonomic constraints.<n>The resulting closed-loop system is formulated as a hybrid dynamical system with continuous swing dynamics and discrete impact events.
• Score: 39.146761527401424
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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