Foot Rotation Indicator (FRI) Point: A New Gait Planning Tool to Evaluate Postural Stability of Biped Robots

The focus of this 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. 1 Motivation The problem of gait planning for biped robots is fundamentally diierent from the path planning for traditional xed-base manipulator arms as succinctly pointed out in 12]. A biped robot may be viewed as a ballistic mechanism which intermittently interacts with its environment { the ground { through its feet. The foot/ground \joint" is unilateral since attractive forces are not present, and underactuated since control inputs are absent. Formally speaking, unilateral-ity and underactuation are the inherent characteristics of the locomotion mechanics and, at the same time, the root causes behind their postural instability and fall. A loss of postural stability may have potentially On leave from: INRIA Rh^ one-Alpes, 38330 Montbonnot Saint Martin, France. serious consequences and this calls for its thorough analysis in order to better predict and eliminate the possibility of fall. Postural balance and stance foot equilibrium are profoundly intertwined. A biped robot gait is said to be statically stable 9] and a human posture is said to be balancedd8] if the ground projection of its center of mass (GCoM) 1 falls within the convex hull of the foot support area (henceforth called the …