Asymptotically Stable Walking for Biped Robots:
Analysis via Systems with Impulse Effects

Jessy Grizzle
Department of EECS
University of Michigan

Biped robots form a subclass of legged or walking robots. The study of
mechanical legged motion has been motivated by its potential use as a
means of
locomotion in rough terrain, as well as its potential benefits to
prothesis
development and testing. This presentation concentrates on issues
related to
the automatic control of biped robots, and more precisely, its primary
goal is
to contribute a means to prove asymptotically stable walking in planar,
under
actuated biped robot models. Since normal walking can be viewed as a
periodic
solution of the robot model, the method of Poincare sections is the
natural
means to study asymptotic stability of a walking cycle. However, due to
the
complexity of the associated dynamic models, this approach has only been
applied successfully to Raibert's one-legged-hopper, and a biped robot
without
a torso. The principal contribution of the present work is to show that
a
control strategy can be designed in a way to greatly simplify the
application
of the method of Poincare to a class of biped models, and in fact, to
reduce
the stability assessment problem to the calculation of a continuous map
from a
sub-interval of the reals to itself. The mapping in question is directly
computable from a simulation model.