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

Systems and Control (eess.SY); Robotics (cs.RO); Dynamical Systems (math.DS); Optimization and Control (math.OC)

arXiv:2603.29050 [eess.SY]

(or arXiv:2603.29050v2 [eess.SY] for this version)

https://doi.org/10.48550/arXiv.2603.29050 Focus to learn more arXiv-issued DOI via DataCite

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