Recoverability estimation and control for an inverted pendulum walker model under foot slip

Locomotion on low-friction surfaces is one of the most challenging problems for bipedal walking. When a stance foot moves and slips on the ground surface, the walker tries to determine whether it is feasible to avoid falling and continue walking. This study uses a simplified two-mass linear inverted pendulum model to analyze the biped dynamics under foot-slip conditions while maintaining closed-form solutions. Using the model, we analytically calculate safe, recoverable, and falling sets to determine whether the walker is able to recover towards a stable position or the fall is inevitable. We present a set of configurations which partition state space and determine the recoverability of the walker. A simple center-of-mass controller is introduced to re-gain the stability by allowing the walker to recover from fall-prone configurations. One attractive property of the developed closed-form expressions lies in feasibility for real-time implementation as a basis for a high-level robust slip recovery controller.