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.