Whole-body balance stability regions for multi-level momentum and stepping strategies

Abstract

A unified framework is established for general balance stability criteria of biped systems. The stability regions of balanced and steppable states are partitions of the center-of-mass (COM) state space that is augmented for general biped systems and tasks. Their boundaries are the set of maximum allowable COM velocity perturbations, under which a specified contact can be maintained (balanced) or a desired step can be made (steppable). Whole-body models with full-order dynamics and system-specific kinematic and actuation limits are established to quantify the effects of momenta and stepping on the system's balance stability under contact interactions. The generality of the framework with respect to systems and tasks is verified with a humanoid robot and a human for walking and standing. Validity and implications of the computed stability regions are demonstrated in the sagittal plane through comparative analyses across strategies and against existing criteria (capturability and zero-moment point), reduced-order models, and simulations. Distinct stability characteristics of experimental walking for the robot (overly balanced) versus humans (unbalanced but steppable) are validated, and the walking principle is analyzed. The partitions also provide inter/intra-region analyses of multi-level momentum and stepping strategies for balancing. A partition-aware controller is implemented for the robot to monitor the stability of the current state and selectively exploit stabilizing actions during simulated standing push recovery.