Stability Criteria of Balanced and Steppable Unbalanced States for Full-Body Systems with Implications in Robotic and Human Gait

Biped walking involves a series of transitions between single support (SS) and double support (DS) contact configurations that can include both balanced and unbalanced states. The new concept of steppability is introduced to partition the set of unbalanced states into steppable states and falling (unsteppable) states based on the ability of a biped system to respond to forward velocity perturbations by stepping. In this work, a complete system-specific analysis of the stepping process including full-order nonlinear system dynamics is presented for the DARwIn-OP humanoid robot and a human subject in the sagittal plane with respect to both balance stability and steppability. The balance stability and steppability of each system are analyzed by numerical construction of its balance stability boundaries (BSB) for the initial SS and final DS contact configuration and the steppable unbalanced state boundary (SUB). These results are presented with center of mass (COM) trajectories obtained from walking experiments to benchmark robot controller performance and analyze the variation of balance stability and steppability with COM and swing foot position along the progression of a step cycle. For each system, DS BSBs were obtained with both constrained and unconstrained arms in order to demonstrate the ability of this approach to incorporate the effects of angular momentum and system-specific characteristics such as actuation torque, velocity, and angle limits.