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

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.

Dual-quaternion learning control for autonomous vehicle trajectory tracking with safety guarantees

We propose a learning-based trajectory tracking controller for autonomous robotic platforms whose motion can be described kinematically on $\mathrm{SE}(3)$. The controller is formulated in the dual quaternion framework and operates at the velocity level, assuming direct command of angular and linear velocities, as is standard in many aerial vehicles and omnidirectional mobile robots. Gaussian Process (GP) regression is integrated into a geometric feedback law to learn and compensate online for unknown, state-dependent disturbances and modeling imperfections affecting both attitude and position, while preserving the algebraic structure and coupling properties inherent to rigid-body motion. The proposed approach does not rely on explicit parametric models of the unknown effects, making it well-suited for robotic systems subject to sensor-induced disturbances, unmodeled actuation couplings, and environmental uncertainties. A Lyapunov-based analysis establishes probabilistic ultimate boundedness of the pose tracking error under bounded GP uncertainty, providing formal stability guarantees for the learning-based controller. Simulation results demonstrate accurate and smooth trajectory tracking in the presence of realistic, localized disturbances, including correlated rotational and translational effects arising from magnetometer perturbations. These results illustrate the potential of combining geometric modeling and probabilistic learning to achieve robust, data-efficient pose control for autonomous robotic systems.