Stable Walking for Bipedal Locomotion under Foot-Slip via Virtual Nonholonomic Constraints
For bipedal robots operating on low-friction terrain, this work provides a control framework that explicitly handles foot slip, a known instability source, but the results are numerical and lack experimental validation.
The paper addresses foot-slip instability in bipedal walking by incorporating slip into the locomotion model via virtual nonholonomic constraints, achieving stable periodic gaits under slip conditions as demonstrated through numerical simulations.
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.