2-D Passive Compass Biped Walker: Analysis and Robustness of Stable Gait

Abstract

The compass-gait biped is a deceptively simple walking machine that is often used as a standard benchmark for testing new concepts and methods in legged locomotion. This study will focus on developing a procedure for finding passive gaits of this specific biped by employing the notion of virtual holonomic constraints. First an introduction to the mathematical foundations behind the basic theory is given, then a rigorous treatment of the hybrid dynamics of the biped and the reduction of the system complexity using virtual holonomic constraints are presented. The reduced dynamics of the biped are used to find relations among the gait parameters leading to the formulation of a minimization problem that yields limit cycle solutions of the hybrid system when solved. The stability of the detected limit cycles is assessed using the notion of transverse linearization, and the procedure for deriving an auxiliary linear system for determining orbital stability of the passive gaits is presented. All major results are visualized and the MATLAB and Maple implementation code is enclosed in either the relevant chapters or the appendixes.