Asymptotically stable walking for biped robots: analysis via systems with impulse effects

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 paper concentrates on issues related to the automatic control of biped robots. 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 Poincaré 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 had limited success. The principal contribution of the present work is to show that the control strategy can be designed in a way that greatly simplifies the application of the method of Poincaré to a class of biped models, and, in fact, to reduce the stability assessment problem to the calculation of a continuous map from a subinterval of IR to itself. The mapping in question is directly computable from a simulation model. The stability analysis is based on a careful formulation of the robot model as a system with impulse effects and the extension of the method of Poincaré sections to this class of models.