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

TLDR

Biped robots, a subclass of legged robots, are studied for their potential in rough‑terrain locomotion and prosthetic development, yet the complexity of their dynamic models has limited the success of traditional stability analyses. The study aims to develop a control strategy that simplifies Poincaré‑based stability analysis for planar, underactuated biped robots, reducing the problem to computing a continuous map from a subinterval of ℝ to itself. The authors formulate the biped model as a system with impulse effects and extend Poincaré sections, enabling the stability assessment to be reduced to computing a continuous map from a subinterval of ℝ to itself directly from a simulation model.

Abstract

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. The 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, underactuated 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 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 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 subinterval of R 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 Poincare sections to this class of models.