Contents 1. INTRODUCTION
Recently, many kinds of biped robots have been developed. Most biped robots are controlled based on ZMP paradigm, but on the other hand another paradigm for design and control of biped robots has been studied. In the early 1990s, Tad McGeer proposed passive dynamic walking model which can walk down a gentle slope without any controller except gravity as an energy source [1]. Since then, many researches have been studied in the domain of human waking and biped robots based on passive dynamic walking. At present passive dynamic walking concept applies not only on a slope but also on a ground using some kinds of actuating strategies. The concept including passive dynamic walking alone and with actuating is so called limit cycle walking lately [5]. Biped robots based on limit cycle walking paradigm commonly need less energy than other bipeds and generate pretty natural gait. To increase performance and to realize a practical biped, the model needs further studies on its stability, disturbance rejection capability, and versatility, the ability to perform various gaits, etc. Stability of limit cycle walking model has been studied and demonstrated with simulations and experiments by many researchers. For example, there are stability analysis of 3D model, the model with upper body, the model having applied actuation, and the model with toed feet etc. In the view of the feet, most of the previous work on limit cycle walking has studied with point or curved feet [2]–[5]. Only a few studies have been done on a flat feet model. And stability properties of the point feet model are well known, compared to those of modified feet model. Although flat feet model have been studied, their stability properties are not clarified especially in the view of bifurcation route to chaos and global stability [6].
