Postural Stability

Postural stability and balance maintenace in human and biped robots

The problem of gait planning for biped robots is fundamentally different from the path planning for traditional fixed-base manipulator arms as succinctly pointed out in Vukobratovic et al. 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, unilaterality 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 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 inter-twined. A biped robot gait is said to be statically stable and a human posture is said to be balanced if the ground projection of its center of mass, GCoM, falls within the convex hull of the foot support area (the support polygon). The exit of the GCoM from the support polygon is equivalent to the presence of an uncompensated moment on the foot which causes it to rotate about a point on the polygon boundary.

Rotational equilibrium of the foot is therefore an important criterion for the evaluation and control of gait, and postural stability in legged robots. Indeed, foot rotation has been noted to reflect a loss of balance and an eventual fall in monopods\cite{Lee and Raibert 91} and bipeds\cite{Arakawa and Fukuda 97} -- two classes of legged robots most prone to instabilities. The exit of the GCoM from the support polygon is considered to be the determining factor of stability in the study of human posture as well\cite{Patla, Frank and Winter 90}.

Although the position of the GCoM is sufficient to determine the occurrence of foot rotation in a stationary robot, it is not so for a robot in motion. Instead it is the location of the foot rotation indicator (FRI) point, which we have introduced, that indicates the existence of an unbalanced torque on the foot. The FRI point is a point on the foot/ground surface, within or outside the support polygon, where the net ground reaction force would have to act to keep the foot stationary. Farther away this point from the support boundary, larger is the unbalanced moment, and greater is the instability. To ensure no foot rotation, the FRI point must remain within the support polygon, regardless of the GCoM position. The FRI point is a dynamics-based criterion, and reduces to the GCoM position for a stationary robot.

We would like emphasize that the FRI point is distinctly different from the center of pressure CoP -- better known as the zero moment point (ZMP) in the robotics literature -- and frequently used in gait planning for biped robots. CoP is a point on the foot/ground surface where the net ground reaction force actually acts. Regardless of the state of stability of the robot, the CoP may never leave the support polygon, whereas the FRI point does so whenever there is an unbalanced torque on the foot. In fact, the distance of the FRI point from the support polygon is an indication of the severity of this unbalanced torque and may be exploited during the planning stage.

Our two main contributions: The first is the introduction of the FRI point which may be employed as a useful tool in gait planning in biped and other legged robots, as well as for the postural stability assessment in the human. The second contribution is in response to our discussion with other researchers regarding the misconceptions surrounding CoP and the CoP/ZMP equivalence. We review the physics behind both the concepts and show that CoP and ZMP are identical.

A list of my papers on this topic:

Postural stability of biped robots and the foot rotation indicator (FRI) point
A. Goswami
International Journal of Robotics Research, Vol. 18, No. 6, 1999.
Foot rotation indicator (FRI) point: A new gait planning tool to evaluate
postural stability of biped robots
A. Goswami
IEEE Int. Conf. on Robotics and Automation, Detroit, May 1999, pp.47-52.
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