  Despite extensive studies on motion stabilization of bipeds, they still
suffer from the lack of disturbance coping capability on slippery surfaces. In
this paper, a novel controller for stabilizing a bipedal motion in its sagittal
plane is developed with regard to the surface friction limitations. By taking
into account the physical limitation of the surface in the stabilization trend,
a more advanced level of reliability is achieved that provides higher
functionalities such as push recovery on low-friction surfaces and prevents the
stabilizer from overreacting. The discrete event-based strategy consists of
modifying the step length and time period at the beginning of each footstep in
order to reestablish stability necessary conditions while taking into account
the surface friction limitation as a constraint to prevent slippage. Adjusting
footsteps to prevent slippage in confronting external disturbances is perceived
as a novel strategy for keeping stability, quite similar to human reaction. The
developed methodology consists of rough closed-form solutions utilizing
elementary math operations for obtaining the control inputs, allowing to reach
a balance between convergence and computational cost, which is quite suitable
for real-time operations even with modest computational hardware. Several
numerical simulations, including push recovery and switching between different
gates on low-friction surfaces, are performed to demonstrate the effectiveness
of the proposed controller. In correlation with human-gait experience, the
results also reveal some physical aspects favoring stability and the fact of
switching between gaits to reduce the risk of falling in confronting different
conditions.
