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This paper introduces a control framework for stable bipedal locomotion that explicitly accounts for foot slippage using virtual nonholonomic constraints to regulate tangential stance-foot velocity. This framework is integrated with virtual holonomic constraints for gait generation, resulting in a hybrid dynamical system. A nonlinear feedback law enforces both constraint types, creating a slip-compatible hybrid zero dynamics manifold, and stability is analyzed using the Poincar\'e map.
Bipedal robots can now walk more stably on slippery surfaces thanks to a new control method that explicitly models and compensates for foot slippage.
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.
