Parametric Walking Patterns and Optimum Atlases for Underactuated Biped Robots

This paper addresses parametric walking patterns and optimum design issues for an underactuated biped robot. The walking pattern is curved by impact postures and middle postures. Impact postures are regulated by two parameters and middle postures are selected to adapt the swing foot to negotiate obstacles. To evaluate constraint conditions, stability margins, and walking performances, some indices are defined, and the correlations between these indices and the two parameters are illustrated by the corresponding atlases. The optimum design method which considers multi-criteria is carried out by using these atlases. This method provides not only one optimum result, but also an optimum region which contains all feasible optimum results. Using these atlases presented in this paper one can obtain the optimum result with respect to any object(s)

I. Introduction

In recent years, the synthesis of walking patterns for underactuated biped robots with point feet has become a popular topic. Without feet, the zero moment point (ZMP) principle [1] is not applicable, and thus the dynamics of effective underactuation must be explicitly addressed in the synthesis of walking pattern. Some works have been devoted to generate walking patterns for underactuated biped robots based on passivity [2]–[4]. McGeer [2] described a natural walking pattern generated by the passive interaction of gravity and inertia on a downhill slope. To clarify the fundamental properties of a passive biped system, Goswami et al. [3], studied dynamic characteristics of a simple compass-type biped mechanism on inclined plane as limit cycle including chaos phenomena. Kajita et al. [4] generated walking patterns by a length varying inverted pendulum. The pendulum's length was varied to maintain the biped's center of mass (COM) a constant height above the walking surface.