Abstract
In the last decade, a number of papers studying from the control theoretical viewpoint the stability and optimization of the walking pattern for biped locomotion systems have been published. Various dynamic models for the biped locomotion have been proposed, but most of them represent only a partial feature of the motion. To express fully both functional and morphological features of the motion, it is necessary to adopt a model with many degrees of freedom. However, such models of a high degree are not adequate for the analysis.
To dissolve such an antinomy, this paper proposes a new method of analyzing the biped locomotion system by the use of singular perturbation. It is shown that if the body mass is sufficiently larger than the leg mass the original biped motion can be represented by two divided modes, a fast mode and a slow mode, owing to the singular perturbation technique. The slow mode corresponds to the angular momentum equation about the center of gravity in regard to the fixed point. The fast mode which decays away rapidly under some conditions represents the fast phenomena of the biped locomotion. Based on this fact, a control algorithm for tracking the trajectory of the motion is presented. Finally, a control law of stabilizing the periodic locomotion (gait stability) is suggested by considering only the slow mode.
