Stabilization of lateral motion in passive dynamic walking

Passive dynamic walking refers to a class of bipedal machines that are able to walk down a gentle slope with no external control or en-ergy input. The legs swing naturally as pendula, and conservation of angular momentum governs the contact of the swing foot with the ground. Previous machines have been limited to planar motions. We extend the planar motions to allow for tilting side to side (roll motion). Passive walking cycles exist, but the roll motion is unsta-ble, resembling that of an inverted pendulum. The instability is due to mismatching of roll velocity with the ground contact conditions. Several strategies are presented for stabilizing this motion, of which the quasi-static control of step width is determined to be both simple and efficient. 1. Passive Dynamic Walking It is possible to construct a two-legged mechanism that can walk down a gentle slope with no energy source other than gravity and no active feedback control (McGeer 1990). The legs swing as coupled pendula so as to produce a stepping motion resembling that of humans (Mochon and McMa-hon 1980), and completion of a step automatically produces the appropriate conditions for the initiation of another step (McGeer 1990). This periodic motion is locally stable in that it passively dampens out small perturbations from its nominal walking trajectory. Its similarity to human walking suggests, first, that humans may harness passive dynamics to some de-gree to aid or simplify control of locomotion and, second, that the grace normally associated with human motion may be attainable by a machine. The study of passive walking may yield insight to automatic control of locomoting machines, as well as physiological motor control of locomoting animals. One particularly attractive feature of the passive walker is that it does not specify a nominal trajectory about which th