Foot rotation indicator (FRI) point: a new gait planning tool to evaluate postural stability of biped robots

Abstract

The focus of the paper is the problem of foot rotation in biped robots during the single support phase. Foot rotation is an indication of postural instability and should be carefully treated in a dynamically stable walk and avoided altogether in a statically stable walk. We introduce the foot rotation indicator (FRI) point which is a point on the foot/ground contact surface where the net ground reaction force would have to act to keep the foot stationary. To ensure no foot rotation, the FRI point must remain within the convex hull of the foot support area. In contrast with the ground projection of the center of mass (GCoM), which is a static criterion, the FRI point incorporates the robot dynamics. As opposed to the center of pressure (CoP)-better known as the zero moment point (ZMP) in the robotics literature-which may not leave the support area, the FRI point may. Due to these important properties the FRI point helps not only to monitor the state of static stability of a biped robot during the entire gait cycle, but indicates the stability robustness or the severity of instability of the gait as well. In response to a recent need the paper also resolves the misconceptions surrounding the CoP/ZMP equivalence.