Dynamics of Bipedal Gait: Part II—Stability Analysis of a Planar Five-Link Biped

Abstract

A general approach based on discrete mapping techniques is presented to study stability of bipedal locomotion. The approach overcomes difficulties encountered by others on the treatment of discontinuities and nonlinearities associated with bipedal gait. A five-element bipedal locomotion model with proper parametric formulation is considered to demonstrate the utility of the proposed approach. Changes in the stability of the biped as a result of bifurcations in the four-dimensional parameter space are investigated. The structural stability analysis uncovered stable gait patterns that conform to the prescribed motion. Stable nonsymmetric locomotion with multiple periodicity was also observed, a phenomenon that has never been considered before. Graphical representation of the bifurcations are presented for direct correlation of the parameter space with the resulting walking patterns. The bipedal model includes some idealizations such as neglecting the dynamics of the feet and assuming rigid bodies. Some additional simplifications were performed in the development of the controller that regulates the motion of the biped.