  Dynamic bipedal robot locomotion has achieved remarkable success due in part
to recent advances in trajectory generation and nonlinear control for
stabilization. A key assumption utilized in both theory and experiments is that
the robot's stance foot always makes no-slip contact with the ground, including
at impacts. This assumption breaks down on slippery low-friction surfaces, as
commonly encountered in outdoor terrains, leading to failure and loss of
stability. In this work, we extend the theoretical analysis and trajectory
optimization to account for stick-slip transitions at point foot contact using
Coulomb's friction law. Using AMBER-3M planar biped robot as an experimental
platform, we demonstrate for the first time a slippery walking gait which can
be stabilized successfully both on a lubricated surface and on a rough no-slip
surface. We also study the influence of foot slippage on reducing the
mechanical cost of transport, and compare energy efficiency in both numerical
simulations and experimental measurements.
